Solving Two-Step Equations

Learn to solve equations that require two operations

Solving Two-Step Equations

What is a Two-Step Equation?

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

Steps to Solve

1. Undo Addition/Subtraction First

Move constants to one side

2. Undo Multiplication/Division Second

Isolate the variable

Example: $3x + 5 = 17$

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

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

Check Your Answer

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

Working with Negatives

Example: $-2x - 6 = 10$

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

Step 2: Divide by -2 $x = -8$

📚 Practice Problems

1Problem 1easy

❓ Question:

Solve: $2x + 7 = 15$

💡 Show Solution

Solution:

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

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

Check: $2(4) + 7 = 8 + 7 = 15$ ✓

Answer: $x = 4$

2Problem 2medium

❓ Question:

Solve: $\frac{x}{4} - 3 = 5$

💡 Show Solution

Solution:

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

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

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

Answer: $x = 32$

3Problem 3hard

❓ Question:

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

💡 Show Solution

Solution:

Let $m$ = number of miles

Equation: $3 + 0.50m = 12$

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

Step 2: Divide by 0.50 $m = 18$

Answer: 18 miles

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