# Algebra Chapter 1-9 Review

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### Write a verbal expression for 6x + 7

Six times x plus seven

### Write a verbal expression for the algebraic expression 5(x² +2)

Five times the quantity x squared plus two

10x

8 + x²

625

3

48

12

137

### Evaluate and name the property used in each step 2 + 6(9− 3²) − 2

2 + 6 (9 − 9) − 2 (sub) . . . . . . . . . . . . . . . . . . . . 2 + 6(0) − 2 (sub) . . . . . . . . . . . . . . . . . . . . . . . . 2 + 0 − 2 (Mult prop of zero). . . . . .. . .. . . . .. . 2-2 (add iden). . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 (sub) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### Find the value for n and name the property 5 · n · 2 = 0

n = 0 multiplication property of zero

### Find the value for n and name the property used: 11· n = 11

n = 1 Multiplicative identity

### Find the value of n and name the property used: 3 · 1/3 = n

n = 1 Multiplicative inverse or reciprocal

53

9x

3x² + 2x + 4

13x + 8y

14x + 35

7

3/2

8

### List the domain and the range for the following relation {(−2,−1), (3, 3), (4,3)}

Domain = {−2, 3, 4} Range = {−1, 3}

### Identify the hypothesis and conclusion for the following relation: If it is Sunday, then mail is not delivered

Hypothesis: It is Sunday Conclusion: mail is not delivered

### Explain the difference between an algebraic expression and a verbal expression.

Algebraic expression consists of numbers, variables, and arithmetic operations. Verbal expression consists of words.

−14

2k − 2

b² + 7

### Determine whether each pair of ratios is an equivalent ratio. 5/9, 7/11

No because when you cross multiply, 55 is not equal to 63

−18

−1, 9/5

− 20

Decrease of 60%

3 hours

14

a = −b/8

m = −8

h = − 6

### Write an equation and solve. X plus 10 is equal to 3 times x.

x + 10 = 3x When the equation is solved, x = 5

### Write an equation and solve. Twenty decreased by three times a number equals −10.

20 − 3x = −10 When the equation is solved, x = 10

16 pounds

\$72.45

\$45.00

11, 12, 13

62, 64

37, 39, 41

x = −6

−51

y = (m − 7x)/3

26

x = −12

All numbers

No solution

### Translate the equation in to a sentence 2x + 10 = 26

Two times x plus ten equals twenty-six or the product of two and x increased by ten is twenty-six.

−6 and 4

0.8

x = −2

3(g + h) = 12

2a + a³ = b

1/2

−4/3

### Determine whether the equation is linear or not. If yes, write the equation in standard form xy = 6

No, because variables are multiplied together

Yes. 3x + y = 2

### Determine whether the equation is linear or not. If yes, write the equation in standard form y = 3x² + 1

No, because the x is raised to a power greater than one

2

2

### Look at problem 11 on page 183. Name the constant of variation. What is the slope?

Constant of variation is −5 The slope is −5

### Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. If y = −4 when x = 2, find y when x = −6.

The equation is y = −2x. The value for y is 12

### Suppose y varies directly as x. Write a direct variation equation that relates x and y. Solve. If y = 7.5 when x = .5, find y when x = −0.3.

The equation is y = 15x. The value for y is −4.5

x = 1/4

r = 2

r = 4

### Graph 2x + 4y = 16 using x an y intercepts

x intercept is 8, and the y intercept is 4. See page 155 and 156 to check the work and graph

### Graph y = 1/3 x + 2 using a table

Some points on the line are (0, 2),(3, 3), (6, 4). Check page 156 to see the graph.

### Graph y = −6x

Some points on the line are (0, 0), (1, −6),(−1, 6) See page 181 for a picture of the graph

14, 12, 10

7.1, 8.1, 9.1

### Write an equation for the nth term of the arithmetic sequence 7, 13, 19, 25 ...

The nth term = 6n + 1

### Write an equation for the nth term of the arithmetic sequence 30, 26, 22, 18 ....

The nth term = −4n + 34

f(x) = 3x − 2

f(x) = −x + 3

(0, 0)

y = kx

### Which of the following equations is a direct variation equation? y = x + 2 or y = 3x

y = 3x because it is of the form y = kx

0

Undefined

−1/3

### Solve the equation 15x −30 = 5x − 50 by graphing and algebraically

Graph f(x) = 10x + 20 and it crosses the x-axis at − 2. Solve 10x + 20 and x = −2

x = 2

### Graph 2x + y = −2 using the x and y intercepts

x intercept is −1 and the y intercept is −2

### Graph y − x = 4 using a table

Solve the equation for y. y = x + 4. Some points on the line are (0, 4), (1, 5), (−1, 3)

### Define slope

(y2 − y1)/(x2 − x1) Other definitions are rise/run and change in y/change in x

### Is the following an arithmetic sequence 1, 4, 9, 16...

No. There is not a common difference.

Slope

y-intercept

3

7

−2

−6

y = −1/5 x + 1

y = −2 x + 3

y = −4/7 x − 2

y = 4x + 5

y = 2x + 1

y = −1/2x + 3

y − 3 = 4(x − 1)

### Look at the graph for problem #42 on page 235. Write the equation in point slope form

y − 7 = −4/3(x + 3)

### Given the point (2, 2) and m = −3, write the equation in point slope form

y − 2 = −3(x − 2)

### Given the point (−8, 5) and m = −2/5, write the equation in point slope form

y − 5 = −2/5(x + 8)

### The point slope form of a linear equation is ________

y - y1 = m(x − x1)

y = mx + b

3x − y = −5

x + y = 12

y = 4x + 6

Parallel

Perpendicular

Neither

### What form should you put lines in to determine if they are parallel, perpendicular, or neither?

Slope intercept form

### What is true about the slopes of parallel lines?

The slopes of parallel lines are the same

### What is true about the slopes of perpendicular lines?

The product of slopes of perpendicular lines is −1. (Slopes of perpendicular lines are opposite reciprocals)

### Write the equations for two lines that are parallel.

There are many answers. An example would by y = 2x and y = 2x + 7.

### Write the equations for two lines that are perpendicular.

There are many answers. An example would by y = 2x and y = −1/2 x + 6. The product of the two slopes has to be −1

### What is true about any horizontal line and a vertical line?

They are perpendicular

y = 3x + 8

y = x − 1

y = 4/5x − 3

y = 3x + 1

### Describe how you would graph y = 1/3 x + 2 using the slope and the y interept.

Put a dot on the y-axis on the number 2. Count a slope of 1/3 by going up 1 and right 3 or down 1 and left 3. Count the slope two or three times and then draw the line.

### Graph 3x − y < 2

Solve the equation for y (slope intercept form) Graph the line with a dotted line. Check a point to see what side to shade. See a graph for this inequality on page 315

### Graph x + 5y ≤ 10

Solve the equation for y (slope intercept form) Graph the line with a solid line. Check a point to see what side to shade. See a graph for this inequality on page 316

### Solve x + 11 > 16 Graph the inequality.

{x|x > 5} The graph of the number line is an open circle on five and shading to the right.

### Solve 3x + 17 < 4x Graph the inequality

{x|x > 17} The graph is a number line with an open circle on 17 and shading to the right.

### Solve the compound inequality x − 5 < − 4 or x − 5 ≥ 1 Graph the compound inequality.

{x | x < 1 or x ≥ 6 The graph is an open circle on 1 and shading to the left and a closed circle on 6 and shading to the right.

### Solve the inequality −2x + 4 > −6 Graph the inequality.

{x | x < 5} The graph is a number line with an open circle on 5 and shading to the left.

### Solve the compound inequality 4 < x + 6 and x + 6 < 5 Graph the inequality

{x | −2 < x < −1 The graph is a number line with an open circle on negative two and an open circle on negative one and shading between

### Write a compound inequality and solve: A number minus one is at most nine, or two times the number is at least twenty-four

x − 1 ≤ 9 or 2x ≥ 24 {x |x ≤ 10 or x ≥12}

### Solve and graph the inequality x + 12 ≥ 8

{x |x ≥ − 4} The graph is a number line with a closed circle on negative four and shading to the right.

### Solve and graph the inequality x − (−5) > −2

{x | x > − 7} The graph is a number line with an open circle on negative seven and shading to the right.

### Wriite and solve in inequality: Twice a number minus 4 is less than three times the nunmber.

2x − 4 < 3x {x | x > − 4}

{x | x ≤ 12}

{x | x > 8}

{x | x> 2}

{x | x > − 3}

{x |x ≥ 5}

{x |x ≤ 24 }

### Graph x > 3 or x ≤ 0

Open circle on three and shading to the right. Closed circle on zero and shading to the left.

### Graph x ≤ 3 and ≥ −2

Closed circle on 3 and closed circle on negative two with shading between

### Solve and graph |x|< 3

{x |−3 < x < 3} Open circle on three and negative three with shading between

### Solve and graph |x − 4|< 4

{x | 0 < x < 8} The number line has an open circle on zero and an open circle on eight with shading between

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