#### Study sets matching "1 algebra linear inequalities"

#### Study sets matching "1 algebra linear inequalities"

coefficient

distributive property

equation

inequality

the numerical part of a term

for any numbers a, b, and c: a(b+c) = ab+bc

a mathematical sentence showing two expressions are equal

mathematical sentences having the symbols <,>

coefficient

the numerical part of a term

distributive property

for any numbers a, b, and c: a(b+c) = ab+bc

parallel lines

perpendicular lines

linear inequality in two variables

solution of an inequality in two varia…

Two different non-vertical lines that have the same slope

Two non-vertical lines in the same plane whose slopes have a…

Can be written in one of the following forms: Ax + By < C, Ax…

One or more ordered pairs that make the inequality true.

parallel lines

Two different non-vertical lines that have the same slope

perpendicular lines

Two non-vertical lines in the same plane whose slopes have a…

Inequality

Set-Builder Notation

Compound Inequality

Intersection

A mathematical sentence that contains less than, greater than…

The expression of the solution set of an inequality, for exam…

Two or more inequalities joined together by "and" or "or"

Where the graphs of two inequalities overlap.

Inequality

A mathematical sentence that contains less than, greater than…

Set-Builder Notation

The expression of the solution set of an inequality, for exam…

System of Equations

System of Inequalities

Consistent

Inconsistent

A set of equations with the same variables.

A set of two or more inequalities with the same variables

A system of equations that has at least one solution is consi…

A system of equations that has no solution.

System of Equations

A set of equations with the same variables.

System of Inequalities

A set of two or more inequalities with the same variables

system of linear equations

solution of a system

elimination method

substitution method

Two or more linear equations using the same variables.

Any ordered pair (x,y) that makes both equations true in a sy…

A method for solving systems by adding or subtracting equatio…

A method for solving systems by replacing one variable with a…

system of linear equations

Two or more linear equations using the same variables.

solution of a system

Any ordered pair (x,y) that makes both equations true in a sy…

Addition property of equality

Subtraction property of equality

Multiplication property of equality

Division property of equality

Add the same quantity (amount) to both sides, and the equatio…

Subtract the same quantity (amount) from both sides, and the…

Multiply both sides of an equation by the same quantity (amou…

Divide both sides of an equation by the same quantity (amount…

Addition property of equality

Add the same quantity (amount) to both sides, and the equatio…

Subtraction property of equality

Subtract the same quantity (amount) from both sides, and the…

Linear Inequality

Solution of a linear inequality

Step 1

Step 2

Similar to a linear equation, but the equal sign is replaced…

Any ordered pair that makes the inequality true.

Solve the inequality for y (slope-intercept form).

Graph the boundary line. Use a solid line for ≤ or ≥. Use a d…

Linear Inequality

Similar to a linear equation, but the equal sign is replaced…

Solution of a linear inequality

Any ordered pair that makes the inequality true.

inequalities

set builder notation

compound inequalities

union

a mathematical sentence involving <, >, or = plus < or >

a notation used to describe the members of a set

Two inequalities that are combined into one statement by the…

The graph of a compound inequality containing "or".

inequalities

a mathematical sentence involving <, >, or = plus < or >

set builder notation

a notation used to describe the members of a set

Linear Inequality

Solution to a Linear Inequality

Solid Line

Dotted Line

a linear equation whose equal sign has been replaced with an…

any ordered pair that makes the inequality true

greater than or equal to, less than or equal to - ordered pai…

greater than, less than - ordered pairs located on the line a…

Linear Inequality

a linear equation whose equal sign has been replaced with an…

Solution to a Linear Inequality

any ordered pair that makes the inequality true

systems of equations

consistent system of equations

Independent system of equations

dependent system of equations

Set of equations with the same variable

A system of equations that is said to have exactly one soluti…

A consistent system of equations with exactly one solution

A system of equations that has an infinite number of solutions.

systems of equations

Set of equations with the same variable

consistent system of equations

A system of equations that is said to have exactly one soluti…

Linear Inequality

Signs

Plotting a Number Line

Peculiarity #1

inequality which involves a linear function.

Signs will vary from > (greater than), < (smaller than), ≥ (g…

While plotting a number line, when a number is greater or sma…

when dividing or multiplying by a negative, the sign of the i…

Linear Inequality

inequality which involves a linear function.

Signs

Signs will vary from > (greater than), < (smaller than), ≥ (g…

function

constant function

identity function

quadratic function

...

f(x)=a ----- where a is any number; horizontal line

f(x)=x ----- which passes through all points coordinates (a,a…

f(x)=x^2 --- graph is symmetrical and is the parent function…

function

...

constant function

f(x)=a ----- where a is any number; horizontal line

equation

expression

inequality

like terms

a combination of numbers, variables, operation symbols and an…

a combination of numbers, variables, operation symbols

a combination of numbers, variables, operation symbols and an…

terms that have the same variables raised to the same exponents

equation

a combination of numbers, variables, operation symbols and an…

expression

a combination of numbers, variables, operation symbols

inequality

solution of an inequality

solution set

graph of an inequality

a mathematical sentence that compares expressions

a value that makes an inequality true

the set of all solutions of an inequality

a graph that shows the solution set

inequality

a mathematical sentence that compares expressions

solution of an inequality

a value that makes an inequality true

CHORD

CIRCLE

LINEAR EQUATION IN STANDARD FORM

MIDPOINT

A LINE SEGMENTWITH END POINTS ON A CIRCLE.

A GEOMETRIC FIGURE CONSISTING OF ALL POINTS P THAT ARE FIXED…

THE FORM AX+BY=C OF A LINEAR EQUATION.

A POINT ON A LINE SEGMENT THAT IS EDUIDISTANT FROM THE END PO…

CHORD

A LINE SEGMENTWITH END POINTS ON A CIRCLE.

CIRCLE

A GEOMETRIC FIGURE CONSISTING OF ALL POINTS P THAT ARE FIXED…

System of Linear Equations

Solution for a System

Infinitely many solutions

Linear Combination

two or more linear equations.

The point of intersection where the lines cross always in the…

When the system of equations have the same slope and y-interc…

It uses addition, subtraction or multiplication to eliminate…

System of Linear Equations

two or more linear equations.

Solution for a System

The point of intersection where the lines cross always in the…

Equation

Solution Set of an Equation

Linear Equation in One Variable

Identity

Mathematical statement that two expressions are equivalent

The value or values of the variable that make the equation true

Can be written in the form ax = b, where a and b are constant…

An equation that is true for all values... Example: x = x

Equation

Mathematical statement that two expressions are equivalent

Solution Set of an Equation

The value or values of the variable that make the equation true

equation

inequality

solving equation or inequality

<

a mathematical sentence that contains an equals sign.

a mathematical sentence that contains less than, greater than…

process of finding the value(s) of a variable that make the e…

"is less than"

equation

a mathematical sentence that contains an equals sign.

inequality

a mathematical sentence that contains less than, greater than…

Domain of a function

Elimination

Independent variable

Output

all the possible x-values of a function (The domain of this s…

used to solve a system of equations by adding the two equatio…

the variable (input) that determines the dependent variable (…

the y-values (range) of a situation (6 and 6.50 are the outpu…

Domain of a function

all the possible x-values of a function (The domain of this s…

Elimination

used to solve a system of equations by adding the two equatio…

Inequality

Variable

Constant

Coefficient

A mathematical sentence that shows the relationship between q…

A letter or symbol used to represent a quantity that can chan…

A value that does not change.

A number multiplied by a variable in an algebraic expression.

Inequality

A mathematical sentence that shows the relationship between q…

Variable

A letter or symbol used to represent a quantity that can chan…

Absolute Value

Algebraic Expression

Coefficient

Constant

the magnitude of a real number without regard to its sign - t…

A mathematical phrase that can contain constants, variables (…

The constant that multiplies the variable in a mathematical e…

A value that does not vary.

Absolute Value

the magnitude of a real number without regard to its sign - t…

Algebraic Expression

A mathematical phrase that can contain constants, variables (…

inequality

solution of an inequality

solution set

graph of an inequality

a mathematical sentence that compares quantities

a value that makes the inequality true

the set of all solutions of an inequality

shows the solution set on a number line

inequality

a mathematical sentence that compares quantities

solution of an inequality

a value that makes the inequality true

parallel lives have the same...

perpendicular lines have...

parallel or perpendicular

paraellel or perpendicular

slope

oppsite (signs) and recipacl ( flip fraction)

y=2x-1... **y=2x

y=2/1x-1... *** y=-1/2x

parallel lives have the same...

slope

perpendicular lines have...

oppsite (signs) and recipacl ( flip fraction)

linear equation

slope

y-intercept

x-intercept

An equation in two variables whose graph in a coordinate plan…

A ratio comparing the change in output over the change in inp…

The value of the output when the input is zero (0, y). The po…

The value of the input when the output is zero (x, 0). The po…

linear equation

An equation in two variables whose graph in a coordinate plan…

slope

A ratio comparing the change in output over the change in inp…

Justin bought 8 sodas and 4 bags of ch…

Emily eanered $10.00 per hour plus a $…

Bryan paid $60 plus $30 per extra person

2 busses and 3 fars hold at most 108 p…

8x+4y=14

Y=10x+15

Y=60+30x

2x+3y< or equal to 108

Justin bought 8 sodas and 4 bags of ch…

8x+4y=14

Emily eanered $10.00 per hour plus a $…

Y=10x+15

"b" in y = mx + b

"m" in y = mx + b

Breakeven point

Correlation

the variable used to represent the y-intercept in a linear fu…

the variable used to represent the slope of a line

the point in which cost = profit

the relationship between a set of data; it can be positive, n…

"b" in y = mx + b

the variable used to represent the y-intercept in a linear fu…

"m" in y = mx + b

the variable used to represent the slope of a line

graph of an inequality with one variable

graph of an inequality with two variab…

Compound Inequality

absolute value equation

On a number line, the set of points that represent all soluti…

Ina coordinate plane, the set of points that represent all so…

Two inequalities joined by and or or.

an equations that contains and absolute value expression

graph of an inequality with one variable

On a number line, the set of points that represent all soluti…

graph of an inequality with two variab…

Ina coordinate plane, the set of points that represent all so…

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

a system of linear equations that has an infinite number of s…

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfies bot…

consistent

a system of linear equations that has at least one ordered pa…

dependent

a system of linear equations that has an infinite number of s…

The number of solutions in a system of…

A system is said to be CONSISTENT if...

A system is said to be INCONSISTENT if…

Echelon Form

None, One, or Infinitely Many

it has one or infinitely many solutions

it has no solution

1- rows of zeroes on the bottom, 2- each leading entry of a r…

The number of solutions in a system of…

None, One, or Infinitely Many

A system is said to be CONSISTENT if...

it has one or infinitely many solutions

System of Linear Equations

Solution for a System

Infinitely many solutions

Elimination Method

two or more linear equations.

The point of intersection where the lines cross always in the…

When the system of equations have the same slope and y-interc…

It uses addition, subtraction or multiplication to eliminate…

System of Linear Equations

two or more linear equations.

Solution for a System

The point of intersection where the lines cross always in the…

Quadrant

Solution of an equation in two variables

Graph of an equation in two variables

Linear equation

One of the four regions into which the x and y axes divide th…

An ordered pair that produces a true statement when the coord…

The set of points in a coordinate plane that represent all so…

An equation whose graph is a line.

Quadrant

One of the four regions into which the x and y axes divide th…

Solution of an equation in two variables

An ordered pair that produces a true statement when the coord…

Domain of a function

Elimination

Independent variable

Output

all the possible x-values of a function (The domain of this s…

used to solve a system of equations by adding the two equatio…

the variable (input) that determines the dependent variable (…

the y-values (range) of a situation (6 and 6.50 are the outpu…

Domain of a function

all the possible x-values of a function (The domain of this s…

Elimination

used to solve a system of equations by adding the two equatio…

Standard Form

Slope-Intercept Form

feasible points

linear inequality

The standard form of a linear equation is Ax + By = C, where…

The slope-intercept form of a linear equation is y = mx + b,…

The set of all solutions that satisfy an equation, and inequa…

A mathematical sentence, such as Ax + By + C < Dx + Ex + F, w…

Standard Form

The standard form of a linear equation is Ax + By = C, where…

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b,…

quadratic equation

quadratic formula

solve an inequality

equivalent inequalities

ax^2 + bx + c = 0... a cannot = 0... two real solutions at most

x = -b +/- √b^2-4ac/ 2a

find all set of values of the variable that make the inequali…

two inequalities that have the same solution set

quadratic equation

ax^2 + bx + c = 0... a cannot = 0... two real solutions at most

quadratic formula

x = -b +/- √b^2-4ac/ 2a

inequality

solution of an inequality

solution set

graph of an inequality

a mathematical sentence that compares expressions

a value that makes an inequality true

the set of all solutions of an inequality

a graph that shows the solution set

inequality

a mathematical sentence that compares expressions

solution of an inequality

a value that makes an inequality true

intercepts

line of best fit

linear function

linear inequality

where the parabola crosses the x-axis; where a line crosses t…

a line that most accurately represents a set of data and is u…

data sets that have a constant rate of change and forms a lin…

an inequality that is the result of replacing the = sign in a…

intercepts

where the parabola crosses the x-axis; where a line crosses t…

line of best fit

a line that most accurately represents a set of data and is u…

"b" in y = mx + b

"m" in y = mx + b

Breakeven point

Correlation

the variable used to represent the y-intercept in a linear fu…

the variable used to represent the slope of a line

the point in which cost = profit

the relationship between a set of data; it can be positive, n…

"b" in y = mx + b

the variable used to represent the y-intercept in a linear fu…

"m" in y = mx + b

the variable used to represent the slope of a line

x < 4

x ≥ 1

all real numbers

x ≤ - 7

Solve the inequality: 10x - 9 < 15 + 4x

Solve the inequality: 2(x - 5) + x ≥ 2x - 9

Solve the compound inequality: x + 18 ≥ 8x + 4 or 15x - 15 ≤…

Solve the compound inequality: 14x + 20 < 14x +16 or 8 - 10x…

x < 4

Solve the inequality: 10x - 9 < 15 + 4x

x ≥ 1

Solve the inequality: 2(x - 5) + x ≥ 2x - 9

Matrix equation

Theorem 3

Identity matrix

Theorem 4

an equation that involves at least one matrix for instance, A…

If A is an m*n matrix, with columns a1...an, and if b is in R…

A square matrix with ones on the diagonal and zeros elsewhere

Let A be an m*n matrix. Then the following statements are log…

Matrix equation

an equation that involves at least one matrix for instance, A…

Theorem 3

If A is an m*n matrix, with columns a1...an, and if b is in R…

Vector Space

Vector Space Axioms

Subspace

Transpose

a set where addition and scalar multiplication as well as the…

1. Commutativity of addition... 2. Associativity in addition... 3.…

a subset of a vector space that is also a vector space closed…

Matrix formed from switching rows and colums (A₁₂)'=A₂₁

Vector Space

a set where addition and scalar multiplication as well as the…

Vector Space Axioms

1. Commutativity of addition... 2. Associativity in addition... 3.…