Problem Description:
The image shows a worksheet titled "One-Step Equations: Integers." The task is to solve each equation for the variable. The equations are listed in two columns, with 12 problems in total.
Solution Approach:
To solve one-step equations involving integers, we need to isolate the variable on one side of the equation. This can be done by performing the inverse operation (addition, subtraction, multiplication, or division) to both sides of the equation. Let's solve each equation step by step.
---
Column 1:
#### 1. \( x + 6 = 13 \)
-
Step: Subtract 6 from both sides.
\[
x + 6 - 6 = 13 - 6
\]
\[
x = 7
\]
#### 2. \( b - 5 = -11 \)
-
Step: Add 5 to both sides.
\[
b - 5 + 5 = -11 + 5
\]
\[
b = -6
\]
#### 3. \( m - 8 = -4 \)
-
Step: Add 8 to both sides.
\[
m - 8 + 8 = -4 + 8
\]
\[
m = 4
\]
#### 4. \( c + 9 = -10 \)
-
Step: Subtract 9 from both sides.
\[
c + 9 - 9 = -10 - 9
\]
\[
c = -19
\]
#### 5. \( y - 7 = 12 \)
-
Step: Add 7 to both sides.
\[
y - 7 + 7 = 12 + 7
\]
\[
y = 19
\]
#### 6. \( g + 7 = -8 \)
-
Step: Subtract 7 from both sides.
\[
g + 7 - 7 = -8 - 7
\]
\[
g = -15
\]
---
Column 2:
#### 7. \( k - 9 = 10 \)
-
Step: Add 9 to both sides.
\[
k - 9 + 9 = 10 + 9
\]
\[
k = 19
\]
#### 8. \( t + 8 = -2 \)
-
Step: Subtract 8 from both sides.
\[
t + 8 - 8 = -2 - 8
\]
\[
t = -10
\]
#### 9. \( p - 3 = -12 \)
-
Step: Add 3 to both sides.
\[
p - 3 + 3 = -12 + 3
\]
\[
p = -9
\]
#### 10. \( r + 5 = -15 \)
-
Step: Subtract 5 from both sides.
\[
r + 5 - 5 = -15 - 5
\]
\[
r = -20
\]
#### 11. \( s - 4 = 11 \)
-
Step: Add 4 to both sides.
\[
s - 4 + 4 = 11 + 4
\]
\[
s = 15
\]
#### 12. \( q + 3 = -7 \)
-
Step: Subtract 3 from both sides.
\[
q + 3 - 3 = -7 - 3
\]
\[
q = -10
\]
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. x = 7 & 7. k = 19 \\
2. b = -6 & 8. t = -10 \\
3. m = 4 & 9. p = -9 \\
4. c = -19 & 10. r = -20 \\
5. y = 19 & 11. s = 15 \\
6. g = -15 & 12. q = -10 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of multi step algebra equations worksheet.
