Chapter 2 Test Review

What is the solution of -3 = x + 5?

• -15

• -8

• 2

• 8

Answer explanation

-3 = x + 5

-3 - 5 = x + 5 - 5 <- We have to subtract 5 from both sides

-8 = x <- now x is by itself :)

Tags

CCSS.6.EE.B.7

What operation should you use to solve -6x = -24

• addition

• subtraction

• multiplication

• division

Answer explanation

To solve for x, we have to DIVIDE both sides by -6.

Tags

CCSS.HSA.REI.A.1

Which of the following solutions is true for $\frac{x}{3}=\frac{1}{4}$  ?

•  $-2\frac{3}{4}$  

•  $\frac{1}{12}$  

•  $\frac{3}{4}$  

•  $3\frac{1}{4}$  

Answer explanation

What do we do here to get x by itself?
We multiply both sides by 3!
 $\frac{x}{3}=\frac{1}{4}$  
 $3\cdot\frac{x}{3}=\frac{1}{4}\cdot3$  
 $x\ =\ \frac{3}{4}$  

Tags

CCSS.4.NF.B.4A

CCSS.4.NF.B.4B

Which property of equality should you use to solve d + 37 = 78?

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve and get x by itself, we'd have to SUBTRACT both sides by 37, so the property of equality we'd use here is Subtraction Property of Equality.

Tags

CCSS.HSA.REI.A.1

What is the solution of -17 = -2n + 13 - 8n?

• -3

• $-\frac{2}{3}$

• 3

• 5

Answer explanation

-17 = -2n + 13 - 8n
First, combine like terms
-17 = (-2n - 8n) + 13
-17 = (-10n) + 13
Now get n by itself!
-17 - 13 = -10n + 13 - 13 <- subtract both sides by 13
-30 = -10n
$\frac{-30}{-10}=\frac{-10n}{-10}$ <- divide both sides by -10
3 = n

Tags

CCSS.8.EE.C.7B

What is the solution of -4(-3m - 2) = 32?

• -2

• 2

• 4

• 6

Answer explanation

-4(-3m - 2) = 32
First, let's distribute that -4 to -3m and -2!
(-4*-3m) + (-4*-2) = 32
12m + 8 = 32
12m + 8 - 8 = 32 - 8 <- Subtract 8 from both sides
12m = 24
$\frac{12m}{12}=\frac{24}{12}$ <- Divide 12 from both sides
m = 2

Tags

CCSS.7.EE.B.4A

What is the solution of

 $\frac{x}{3}+\frac{3}{5}=-\frac{1}{15}$  ?

• -2
  

•  $\frac{8}{5}$  

• 2

•  $\frac{16}{3}$  

Answer explanation

 $\frac{x}{3}+\frac{3}{5}=-\frac{1}{15}$  
 $\frac{x}{3}+\frac{3}{5}-\frac{3}{5}=-\frac{1}{15}-\frac{3}{5}$  <- subtract 3/5 from both sides
 $\frac{x}{3}=-\frac{1}{15}-\frac{3}{5}$  
 $\frac{x}{3}=-\frac{1}{15}-\frac{9}{15}$  <- change 3/5 to 9/15 so we can subtract!
 $\frac{x}{3}=-\frac{10}{15}$  <- (-1 - 9) is -10!
 $3\cdot\frac{x}{3}=-\frac{10}{15}\cdot3$  <- multiply both sides by 3

 $x\ =\ -\frac{30}{15}$  
x = -2

Tags

CCSS.7.EE.B.4A

What is the solution of -8x - 5 + 3x = 7 + 4x - 9?

• -3

• $-\frac{1}{3}$

• $\frac{1}{3}$

• 3

Answer explanation

We want to get the variable x together on one side!
-8x - 5 + 3x = 7 + 4x - 9
First, let's combine like terms
(-8x + 3x) -5 = 4x + (7 - 9)
-5x - 5 = 4x - 2
-5x - 4x - 5= 4x - 4x - 2 <- subtract both sides by 4x
-9x - 5 = -2
-9x - 5 + 5 = -2 + 5 <- add both sides by 5
-9x = 3
$\frac{-9x}{-9}=\frac{3}{-9}$ <- divide both sides by -3
x = $-\frac{1}{3}$

What is the solution of -(-5 - 6x) = 4(5x + 3)?

• -2

•  $-\frac{1}{2}$  

•  $\frac{1}{2}$  

• 2

Answer explanation

-(-5 - 6x) = 4(5x + 3)
First, let's distribute the -1 on the one side and the 4 on the other side!
(-1 * -5) + (-1 * -6x) = (4 * 5x) + (4 * 3)
5 + 6x = 20x + 12
Now, let's get x to one side!
5 + 6x - 20x = 20x - 20x + 12 <- subtract 20x from both sides
5 - 14x = 12
5 - 5 - 14x = 12 - 5 <- subtract 5 from both sides
-14x = 7
 $\frac{-14x}{-14}=\frac{7}{-14}$  <- divide both sides by -14
x =  $-\frac{1}{2}$  

Tags

CCSS.8.EE.C.7B

What is the solution of 2n - 3(4n + 5) = -6 (n - 3) - 1?

• -8

• -6

• $-\frac{1}{2}$

• 4

Answer explanation

2n - 3(4n + 5) = -6(n - 3) - 1

First, let's distribute
2n + (-3 * 4n) + (-3 * 5) = (-6 * n) + (-6 * -3) - 1
2n - 12n -15 = -6n + 18 - 1
Let's combine like terms!
(2n - 12n) - 15 = -6n + (18 - 1)
-10n - 15 = -6n + 17
Let's get n on one side!
-10n + 6n - 15 = -6n + 6n + 17 <- add 6n on both sides
-4n - 15 = 17
-4n - 15 + 15 = 17 + 15 <- add 15 on both sides
-4n = 32
$\frac{-4n}{-4}=\frac{32}{-4}$
n = -8