7.EE.B.4a 7th Grade Expressions & Equations

Two-Step Equations

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, and compare an algebraic solution to an arithmetic one.

How to explain it

The anchor students hold onto: Undo addition or subtraction first, then divide by the coefficient. For p(x + q) = r, distribute first or divide both sides by p. Always check by substituting your answer back.

Two-step equations underlie multi-step equations, variables on both sides, and literal equations in Algebra 1. The form p(x + q) = r links the distributive property to multi-step solving.

Worked examples

Example 1 Standard Form

Solve: 3x + 5 = 20.

Step 1Subtract 5: 3x = 15.

Step 2Divide by 3: x = 5.

Step 3Check: 3(5) + 5 = 20.

Answerx = 5

Example 2 Distributive Form

Solve: 2(x + 3) = 14.

Step 1Distribute: 2x + 6 = 14.

Step 2Subtract 6: 2x = 8.

Step 3Divide by 2: x = 4.

Answerx = 4

Example 3 Word Problem

Word problem: 4x + 8 = 32.

Step 1A reader has 8 pages done and reads 4 per day.

Step 2She wants 32 pages total.

Step 3Subtract 8: 4x = 24.

Step 4Divide by 4: x = 6.

Step 5She needs 6 days.

Answerx = 6 (6 days)

Common mistakes

What students write Divides before undoing the constant term.

The fix Undo + or - first, then divide to isolate x.

What students write Distributes p(x + q) to the first term only.

The fix Multiply the factor by BOTH terms inside.

Teacher tip

Head off the two predictable errors before they happen. First: Undo + or - first, then divide to isolate x. Second: Multiply the factor by BOTH terms inside.