Two-Step Equations

Two-step equations require two inverse operations to solve.

General Strategy

The standard form is: $ax + b = c$

Steps:

1. Undo addition/subtraction first
2. Then undo multiplication/division

This is the reverse of order of operations!

Examples

Example 1: $2x + 5 = 13$

Step 1: Subtract 5 from both sides $2x + 5 - 5 = 13 - 5$ $2x = 8$

Step 2: Divide both sides by 2 $\frac{2x}{2} = \frac{8}{2}$ $x = 4$

Check: $2(4) + 5 = 8 + 5 = 13$ ✓

Example 2: $\frac{x}{3} - 4 = 2$

Step 1: Add 4 to both sides $\frac{x}{3} - 4 + 4 = 2 + 4$ $\frac{x}{3} = 6$

Step 2: Multiply both sides by 3 $3 \cdot \frac{x}{3} = 3 \cdot 6$ $x = 18$

Check: $\frac{18}{3} - 4 = 6 - 4 = 2$ ✓

Example 3: $-3x + 7 = -2$

Step 1: Subtract 7 from both sides $-3x + 7 - 7 = -2 - 7$ $-3x = -9$

Step 2: Divide both sides by -3 $\frac{-3x}{-3} = \frac{-9}{-3}$ $x = 3$

Check: $-3(3) + 7 = -9 + 7 = -2$ ✓

Summary

1. Deal with constants first (add/subtract)
2. Deal with coefficients second (multiply/divide)
3. Always check your answer!