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

Two-Step Inequalities

Solve word problems leading to inequalities of the form px + q > r or px + q < r, graph the solution set, and interpret it in context.

How to explain it

The anchor students hold onto: Undo addition or subtraction first, then multiplication or division. Divide by a NEGATIVE — FLIP the sign. Graph: open circle for < or >; closed circle for ≤ or ≥.

Two-step inequalities lead to multi-step and compound inequalities in Algebra 1 and graphing solution regions. The flip rule is foundational for linear inequalities in two variables.

Worked examples

Example 1 No Flip

Solve and graph: 2x + 3 > 11.

Step 1Subtract 3: 2x > 8.

Step 2Divide by 2: x > 4.

Step 3Graph: open circle at 4, shade right.

Answerx > 4

Example 2 Flip Required

Solve and graph: -3x + 1 ≥ 10.

Step 1Subtract 1: -3x ≥ 9.

Step 2Divide by -3 → FLIP the sign.

Step 3x ≤ -3.

Step 4Graph: closed circle at -3, shade left.

Answerx ≤ -3

Example 3 Word Problem

Word problem: 5x + 15 ≥ 50.

Step 1A student earns 5 pts per quiz, starts with 15 bonus pts.

Step 2She needs at least 50 pts total.

Step 3Subtract 15: 5x ≥ 35.

Step 4Divide by 5: x ≥ 7.

Step 5She needs at least 7 quizzes.

Answerx ≥ 7 (at least 7 quizzes)

Common mistakes

What students write Divides by negative but forgets to flip the sign.

The fix Divide by a negative — REVERSE the inequality sign.

What students write Solves correctly but shades in the wrong direction.

The fix x > n or ≥ n: shade right. x < n or ≤ n: shade left.

Teacher tip

Head off the two predictable errors before they happen. First: Divide by a negative — REVERSE the inequality sign. Second: x > n or ≥ n: shade right. x < n or ≤ n: shade left.