Problem Description:
The task involves solving two-step equations. The goal is to isolate the variable on one side of the equation by performing operations that maintain the equality. The worksheet provides examples and practice problems, along with instructions to guide the solution process.
Key Instructions:
1.
Add or subtract the same value from both sides to simplify the equation.
2.
Multiply or divide both sides by the same non-zero value to solve for the variable.
Practice Problems:
We will solve each problem step by step.
---
####
Problem 1: Solve \( x + 7 = 20 \)
1.
Step 1: Subtract 7 from both sides to isolate \( x \).
\[
x + 7 - 7 = 20 - 7
\]
Simplify:
\[
x = 13
\]
2.
Final Answer:
\[
\boxed{13}
\]
---
####
Problem 2: Solve \( 5x = 40 \)
1.
Step 1: Divide both sides by 5 to isolate \( x \).
\[
\frac{5x}{5} = \frac{40}{5}
\]
Simplify:
\[
x = 8
\]
2.
Final Answer:
\[
\boxed{8}
\]
---
####
Problem 3: Solve \( x - 6 = 15 \)
1.
Step 1: Add 6 to both sides to isolate \( x \).
\[
x - 6 + 6 = 15 + 6
\]
Simplify:
\[
x = 21
\]
2.
Final Answer:
\[
\boxed{21}
\]
---
####
Problem 4: Solve \( 4x = 32 \)
1.
Step 1: Divide both sides by 4 to isolate \( x \).
\[
\frac{4x}{4} = \frac{32}{4}
\]
Simplify:
\[
x = 8
\]
2.
Final Answer:
\[
\boxed{8}
\]
---
####
Problem 5: Solve \( x + 9 = 25 \)
1.
Step 1: Subtract 9 from both sides to isolate \( x \).
\[
x + 9 - 9 = 25 - 9
\]
Simplify:
\[
x = 16
\]
2.
Final Answer:
\[
\boxed{16}
\]
---
####
Problem 6: Solve \( 3x = 27 \)
1.
Step 1: Divide both sides by 3 to isolate \( x \).
\[
\frac{3x}{3} = \frac{27}{3}
\]
Simplify:
\[
x = 9
\]
2.
Final Answer:
\[
\boxed{9}
\]
---
####
Problem 7: Solve \( x - 4 = 12 \)
1.
Step 1: Add 4 to both sides to isolate \( x \).
\[
x - 4 + 4 = 12 + 4
\]
Simplify:
\[
x = 16
\]
2.
Final Answer:
\[
\boxed{16}
\]
---
####
Problem 8: Solve \( 6x = 42 \)
1.
Step 1: Divide both sides by 6 to isolate \( x \).
\[
\frac{6x}{6} = \frac{42}{6}
\]
Simplify:
\[
x = 7
\]
2.
Final Answer:
\[
\boxed{7}
\]
---
Summary of Solutions:
1. \( x + 7 = 20 \) → \( \boxed{13} \)
2. \( 5x = 40 \) → \( \boxed{8} \)
3. \( x - 6 = 15 \) → \( \boxed{21} \)
4. \( 4x = 32 \) → \( \boxed{8} \)
5. \( x + 9 = 25 \) → \( \boxed{16} \)
6. \( 3x = 27 \) → \( \boxed{9} \)
7. \( x - 4 = 12 \) → \( \boxed{16} \)
8. \( 6x = 42 \) → \( \boxed{7} \)
Final Boxed Answers:
\[
\boxed{13, 8, 21, 8, 16, 9, 16, 7}
\]
Parent Tip: Review the logic above to help your child master the concept of 8th grade math worksheet algebra.
