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Solving Two-Step Equations

Learn to solve equations that require two operations

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Solving Two-Step Equations

What is a Two-Step Equation?

An equation that requires two operations to solve: 3x+5=173x + 5 = 17

Steps to Solve

1. Undo Addition/Subtraction First

Move constants to one side

2. Undo Multiplication/Division Second

Isolate the variable

Example: 3x+5=173x + 5 = 17

Step 1: Subtract 5 from both sides 3x=123x = 12

Step 2: Divide both sides by 3 x=4x = 4

Check Your Answer

Substitute back into the original equation: 3(4)+5=12+5=173(4) + 5 = 12 + 5 = 17 ✓

Working with Negatives

Example: −2x−6=10-2x - 6 = 10

Step 1: Add 6 to both sides −2x=16-2x = 16

Step 2: Divide by -2 x=−8x = -8

📚 Practice Problems

1Problem 1easy

❓ Question:

Solve: 2x+7=152x + 7 = 15

💡 Show Solution

Solution:

Step 1: Subtract 7 from both sides 2x=82x = 8

Step 2: Divide both sides by 2 x=4x = 4

Check: 2(4)+7=8+7=152(4) + 7 = 8 + 7 = 15 ✓

Answer: x=4x = 4

2Problem 2easy

❓ Question:

Solve: 2x+7=152x + 7 = 15

💡 Show Solution

Solution:

Step 1: Subtract 7 from both sides 2x=82x = 8

Step 2: Divide both sides by 2 x=4x = 4

Check: 2(4)+7=8+7=152(4) + 7 = 8 + 7 = 15 ✓

Answer: x=4x = 4

3Problem 3medium

❓ Question:

Solve: x4−3=5\frac{x}{4} - 3 = 5

💡 Show Solution

Solution:

Step 1: Add 3 to both sides x4=8\frac{x}{4} = 8

Step 2: Multiply both sides by 4 x=32x = 32

Check: 324−3=8−3=5\frac{32}{4} - 3 = 8 - 3 = 5 ✓

Answer: x=32x = 32

4Problem 4medium

❓ Question:

Solve: x4−3=5\frac{x}{4} - 3 = 5

💡 Show Solution

Solution:

Step 1: Add 3 to both sides x4=8\frac{x}{4} = 8

Step 2: Multiply both sides by 4 x=32x = 32

Check: 324−3=8−3=5\frac{32}{4} - 3 = 8 - 3 = 5 ✓

Answer: x=32x = 32

5Problem 5hard

❓ Question:

A taxi charges \3plusplus$0.50permile.Ifthetotalfarewasper mile. If the total fare was$12$, how many miles was the trip?

💡 Show Solution

Solution:

Let mm = number of miles

Equation: 3+0.50m=123 + 0.50m = 12

Step 1: Subtract 3 from both sides 0.50m=90.50m = 9

Step 2: Divide by 0.50 m=18m = 18

Answer: 18 miles

6Problem 6hard

❓ Question:

A taxi charges \3plusplus$0.50permile.Ifthetotalfarewasper mile. If the total fare was$12$, how many miles was the trip?

💡 Show Solution

Solution:

Let mm = number of miles

Equation: 3+0.50m=123 + 0.50m = 12

Step 1: Subtract 3 from both sides 0.50m=90.50m = 9

Step 2: Divide by 0.50 m=18m = 18

Answer: 18 miles

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❓ Frequently Asked Questions

What is Solving Two-Step Equations?▾
Learn to solve equations that require two operations
How can I study Solving Two-Step Equations effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Solving Two-Step Equations study guide free?▾
Yes — all study notes, flashcards, and practice problems for Solving Two-Step Equations on Study Mondo are free to access. No account is needed.
What course covers Solving Two-Step Equations?▾
Solving Two-Step Equations is part of the Grade 8 Math course on Study Mondo, specifically in the Linear Equations and Functions section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Solving Two-Step Equations?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.