14 terms

Inequality Symbols

Just as the symbol "=" is used in mathematics to represent that two quantities are equal, greater than and less than symbols can be used to describe the relationships between quantities that are not equal.

Variable

A letter or symbol that represents one or more numbers.

Expression

A combination of numbers, variables, and operation symbols. It does not contain an equal sign. For example: 2x + 3(5 − 2x) + 8.

Terms

Parts of the expression separated by addition and subtraction. For example, in the expression 2x + 3(5 - 2x) + 8, 2x, 3(5 − 2x), and 8 are examples.

Coefficient

A number multiplying a variable or product of variables. In the expression 2x, 2 is an example of this.

Constant Term

A number that is not multiplied by a variable. In the expression 2x + 3x + 8, 8 is an example of this.

Factor

Part of a multiplication expression. In the expression 3(5 - 2x), 3 and 5 - 2x are both examples of this.

How to graph inequalities

1) Treat the problem as if it were an equality and solve the problem. The solution to the equality is called the boundary point.

2) Place your boundary point on the number line as a point or CLOSED circle.

3) Test one value on either side in the original inequality by substituting it into the original inequality. This will determine which set of numbers makes the inequality true.

4) Write the inequality solution and extend an arrow onto the number line in the direction of the side that makes the inequality true.

NOTE: When the inequality is < or >, the boundary point is not included in the answer. On a number line, this would be indicated with an OPEN circle.

2) Place your boundary point on the number line as a point or CLOSED circle.

3) Test one value on either side in the original inequality by substituting it into the original inequality. This will determine which set of numbers makes the inequality true.

4) Write the inequality solution and extend an arrow onto the number line in the direction of the side that makes the inequality true.

NOTE: When the inequality is < or >, the boundary point is not included in the answer. On a number line, this would be indicated with an OPEN circle.

Factoring

The process of writing an expression in the form of factors--using multiplication like 3(x + 1). Though 3(x+1) could also be written as 3x + 3 by using the Distributive Property, the expression 3(x + 1) is a product and is written in factored form, while 3x + 3 is a sum.

Equations ALWAYS have..

an equal sign!

Inequalities NEVER have...

an equal sign! Instead they have one of the inequality signs.

To solve an equation or inequality means to...

Find all values of the variable that make the relationship true. The solution can be shown on a number line.

How to Check a Solution

Substitute the solution into the equation and verify that it makes the two sides of the equation equal.

For example, to verify that x = 10 is a solution to the equation 3(x − 5) = 15, substitute 10 into the equation for x.

For example, to verify that x = 10 is a solution to the equation 3(x − 5) = 15, substitute 10 into the equation for x.

Solutions to Equations with one Variable

A solution to an equation gives the value(s) of the variable that makes the equation true.

Some equations have several solutions, such as x2 = 25, where x = 5 or −5.

Some equations may also have no solution or an infinite (unlimited) number of solutions.

Some equations have several solutions, such as x2 = 25, where x = 5 or −5.

Some equations may also have no solution or an infinite (unlimited) number of solutions.