The image provided is a math worksheet titled "Two Step Equation - Integers," which involves solving equations with integers. Below, I will explain the solution process for each equation step by step.
---
Equation 1:
\[
-14y = -104 - y
\]
1. Add \( y \) to both sides:
\[
-14y + y = -104
\]
\[
-13y = -104
\]
2. Divide both sides by \(-13\):
\[
y = \frac{-104}{-13}
\]
\[
y = 8
\]
---
Equation 2:
\[
-63d = 96 - 55d
\]
1. Add \( 55d \) to both sides:
\[
-63d + 55d = 96
\]
\[
-8d = 96
\]
2. Divide both sides by \(-8\):
\[
d = \frac{96}{-8}
\]
\[
d = -12
\]
---
Equation 3:
\[
10x - 154 = -4x
\]
1. Add \( 4x \) to both sides:
\[
10x + 4x - 154 = 0
\]
\[
14x - 154 = 0
\]
2. Add \( 154 \) to both sides:
\[
14x = 154
\]
3. Divide both sides by \( 14 \):
\[
x = \frac{154}{14}
\]
\[
x = 11
\]
---
Equation 4:
\[
-88 + 11p = 22p
\]
1. Subtract \( 11p \) from both sides:
\[
-88 = 22p - 11p
\]
\[
-88 = 11p
\]
2. Divide both sides by \( 11 \):
\[
p = \frac{-88}{11}
\]
\[
p = -8
\]
---
Equation 5:
\[
-12z = -204 - 24z
\]
1. Add \( 24z \) to both sides:
\[
-12z + 24z = -204
\]
\[
12z = -204
\]
2. Divide both sides by \( 12 \):
\[
z = \frac{-204}{12}
\]
\[
z = -17
\]
---
Equation 6:
\[
36t = 184 + 28t
\]
1. Subtract \( 28t \) from both sides:
\[
36t - 28t = 184
\]
\[
8t = 184
\]
2. Divide both sides by \( 8 \):
\[
t = \frac{184}{8}
\]
\[
t = 23
\]
---
Equation 7:
\[
29b = -31b + 240
\]
1. Add \( 31b \) to both sides:
\[
29b + 31b = 240
\]
\[
60b = 240
\]
2. Divide both sides by \( 60 \):
\[
b = \frac{240}{60}
\]
\[
b = 4
\]
---
Equation 8:
\[
-26f - 135 = -31f
\]
1. Add \( 31f \) to both sides:
\[
-26f + 31f - 135 = 0
\]
\[
5f - 135 = 0
\]
2. Add \( 135 \) to both sides:
\[
5f = 135
\]
3. Divide both sides by \( 5 \):
\[
f = \frac{135}{5}
\]
\[
f = 27
\]
---
Equation 9:
\[
21c = -255 + 4c
\]
1. Subtract \( 4c \) from both sides:
\[
21c - 4c = -255
\]
\[
17c = -255
\]
2. Divide both sides by \( 17 \):
\[
c = \frac{-255}{17}
\]
\[
c = -15
\]
---
Equation 10:
\[
324 + m = -8m
\]
1. Add \( 8m \) to both sides:
\[
324 + m + 8m = 0
\]
\[
324 + 9m = 0
\]
2. Subtract \( 324 \) from both sides:
\[
9m = -324
\]
3. Divide both sides by \( 9 \):
\[
m = \frac{-324}{9}
\]
\[
m = -36
\]
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Parent Tip: Review the logic above to help your child master the concept of 12 grade math worksheet.
