Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free inequalities worksheet for grades 6-7 builds confidence with solving and graphing linear inequalities.

Lesson plan snapshot

15-20 min

Warm-up (3 min): review inequality symbols and what they mean.
Model (5 min): solve the worked example together.
Guided practice (5 min): complete problems 1-3 as a group.
Independent practice (7 min): finish the remaining problems.

Materials: number line, pencil

Learning targets

Solve one-step inequalities using inverse operations.
Solve two-step inequalities and know when to flip the sign.
Graph solutions with open or closed circles and arrows.

Step-by-step approach

1Identify the operation applied to the variable.
2Undo addition or subtraction first, then multiplication or division.
3Flip the inequality sign when multiplying or dividing by a negative.
4Graph the solution with an open or closed circle and an arrow.

Common mistakes

Mistake

Forgetting to flip the inequality sign with negatives.

Try instead

Multiply or divide by a negative? Flip the sign every time.

Mistake

Using a closed circle for > or <.

Try instead

Use open circles for > or < and closed circles for >= or <=.

Mistake

Giving one number instead of a range.

Try instead

Keep the inequality sign in your final answer.

Worked example

Guided

Solve:

-3x + 6 \le 12

Subtract 6 from both sides: -3x <= 6.
Divide by -3 and flip the sign: x >= -2.

Answer:

x \ge -2

Related resources

Equations

Solve one- and two-step equations with clear steps.

View resource

Integers

Number line reasoning and integer operations.

View resource

Expressions

Combine like terms and distribute accurately.

View resource

Practice problems

10 problems • 15 min

Printable worksheet

1
Solve for $x$ : $x - 9 < -7$
2
Solve for $x$ : $x + 6 > 0$
3
Solve for $x$ : $4x - 4 \ge 24$
4
A number line shows an closed circle at -4 with shading to the right. Write the inequality.
5
Graph $x \le 2$ on a number line.
6
Solve for $x$ : $2x - 3 \le -5$
7
Solve for $x$ : $8x \le -32$
8
Solve for $x$ : $6x - 1 \le -13$
9
Solve for $x$ : $-6x > 12$
10
Solve for $x$ : $-4x \ge 20$

Answer key

10 answers

11) $x < 2$
22) $x > -6$
33) $x \ge 7$
44) $x \ge -4$
55) Closed circle at 2, shade left.
66) $x \le -1$
77) $x \le -4$
88) $x \le -2$
99) $x < -2$
1010) $x \le -5$

Teacher tips

TUse a symbol chart for <, >, <=, >= before solving.
THave students say 'flip the sign' when dividing by negatives.
TModel open vs closed circles on a number line.

Parent tips

PAsk your child why the sign flips with negatives.
PPractice graphing two inequalities on scratch paper.
PCheck that the answer is a range, not just one number.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).