Free Printable Unit 6 Study Guide - Expressions, Equations, Inequalities

1.

$5^2-7\left(5-1+3\right)$ Simplify:

(a)

2.

$6\left|-4+3\right|+8\div2$ Simplify:

(a)

3.

Choose the inequalilty that says: 16 subtracted from a number is more than 15

a)

16 - n > 15

b)

n - 16 > 15

c)

n - 16 ≥ 15

d)

n - 16 < 15

4.

Which expression bests represents "the difference of 6 and half a number"?

a)

$6-\frac{1}{2}x$

b)

$\frac{1}{2}x-6$

c)

2x-6

d)

6-2x

5.

Ms. Sisson is grocery shopping and has a budget of $50. She is buying eggs which are $6 per pack and her other groceries cost her $32. How many packs of eggs can she buy to stay in her budget? Is this and equation or inequality? Write the algebraic problem and solve, using "p" as your variable.

a)

Equation

6p + 50 = 32

p = 3

b)

Inequality

6p + 32 > 50

p ≥ 3

c)

Inequality

32 + 6p ≤ 50

p ≤ 3

d)

Equation

32 + 6p = 50

p = 3

6.

Select all the phrases that could represent the following expression: 2x+10

a)

Double a number and ten

b)

The difference between twice a number and ten

c)

Twice a number plus 10

d)

Double the sum of a number and ten

e)

Two times a number increased by ten

7.

$-3v-b^2+bv$ Simplify the expression when b = -3 and v = $\frac{2}{3}$

(a)

8.

$\frac{1}{2}\left(4r^2-2r\right)$

Which number could replace the variable to make the expression equivalent to 6?

a)

-2

b)

-1

c)

1

d)

2

9.

Beatrice has 18 pencils. Beatrice has 2 more than 4 times the number of pencils Rick has. Exactly how many pencils does Rick have?

a)

11 pencils

b)

7 pencils

c)

5 pencils

d)

4 pencils

10.

$\frac{d}{3}+8=12$

Which phrase best represents the equation?

a)

Eight more than the quotient of a number, d, and three is twelve.

b)

Eight more than the difference of a number, d, and three is twelve.

c)

The quotient of eight more than a number, d, and three is twelve.

d)

The difference of eight more than a number, d, and three is twelve.

11.

$\frac{d-3.4}{7}=2.8$

Find the solution to the number sentence.

a)

d = 30

b)

d = 3.8

c)

d = 16.2

d)

d = 23.0

12.

Clinton earns $12 per hour cutting grass. He earned a total of $162 last week cutting grass. Exactly how many hours did he spend cutting grass last week?

Answer: (a) hours (enter a number only)

13.

(a)

14.

Solve the following problem. *HINT: Combine like terms first

14x + 7 - 3 - 8x = 7 - 1

a)

x = 1/3

b)

x = 3

c)

x = -5/3

d)

x = -1/3

15.

Which equation and solution is represented by the model?

a)

2x - 3 = 9, x = 6

b)

2x - 3 = 9, x = 3

c)

-2x + 3 = 9, x = 6

d)

-2x - 3 = 9, x = 3

16.

Quami earns $10 helping his friend clean windows during his summer vacation. He charges $1 for the first window and $0.50 for each additional window (x) he washes. Select the correct equation and solution.

a)

0.5x + 1 = 10, x = 18

b)

0.5x = 10, x = 4.5

c)

x + 1 = 10, x = 9

d)

x + 0.5 = 10, x = 9.5

17.

Samuel helps his brother paint walls during his summer vacation. He charges $10 for the first room and $5 for each additional room (x) he paints. Which equation could Samuel use to find out how many additional rooms he would have to paint to make $50 at one house?

a)

5x + 10 = 50

b)

5x = 50

c)

10x + 5 = 50

d)

x + 10 = 50

18.

What value of x satisfies the equation:

4x - 8 = 20

a)

7

b)

3

c)

-3

d)

-7

19.

Which of the following represents "four less than five times a number is 41", and its solution?

a)

4 - 5x = 41; x = -7.4

b)

4 - 5x = 41; x = 9

c)

5x - 4 = 41; x = 9

d)

5x - 4 = 41; x = 7.4

20.

$-3a+\frac{1}{2}\le8$ Which graph best represents the solution to the inequality?

a)

b)

c)

d)

21.

$6\ge\frac{1}{2}x+21$

What is the solution to the inequality?

a)

$-30\le x$

b)

$-27\le x$

c)

$-30\ge x$

d)

$-27\ge x$

22.

$-6x+18\le12$

Which graph represents the solution to the inequality?

a)

b)

c)

d)

23.

$10<\frac{n}{2}-4$

Which of the following could be a solution to the inequality?

a)

8

b)

20

c)

28

d)

31

24.

$-7x+13<55$

What is the solution to the inequality?

a)

$x>-6$

b)

$x<-6$

c)

$x>6$ x

d)

$x<6$

25.

$-2x-8\le10$

Solve the inequality and choose ALL the correct solutions.

a)

-10

b)

9

c)

-9

d)

0

e)

-21

26.

$4x-8\ge8$

Which graph represents the solution to the inequality?

a)

b)

c)

d)

27.

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

28.

$-3x<15$

Which graph represents the solution set for the inequality?

a)

b)

c)

d)

29.

$x\le-9$

Select ALL of the characteristics of the graph for the inequality.

a)

Circle is open

b)

Circle is closed

c)

Graph shaded (arrow) to the right of the circle

d)

Graph shaded (arrow) to the left of the circle

30.

Select the inequality that would be written as: "the product of a number and 2 is at least 10"

a)

$2+n>10$

b)

$2n>10$

c)

$2n\ge10$

d)

$2+n\ge10$

31.

Select the inequality that would be written as:

9 less than a number is at most 2

a)

$x-9\le2$

b)

$9-x\le2$

c)

$x-9>2$

d)

$9-x>2$

Unit 6 Study Guide - Expressions, Equations, Inequalities

Total questions: 31

Worksheet time: 17mins

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