Inequalities · One-step · 2.2

Multiply or divide.

To undo multiplication, divide both sides (and vice-versa). Dividing or multiplying by a POSITIVE number keeps the inequality direction. 3x ≤ 12 → x ≤ 4.

01 / THE IDEA

See it work.

Watch the method

Multiply or divide

3x ≤ 12 → divide by 3 → x ≤ 4.

1 / 2
3x≤123x \le 12
1

The inequality

Solve for x just like an equation — with one twist.

3x≤123x \le 12
2

Isolate x

Undo the operations to get x alone (the sign stays the same).

x≤4x ≤ 4

On the number line

Shade the solutions.

A closed circle includes 4; the arrow points to every value that works.

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02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

Type the solution, e.g. x < 4 (you can write <= for ≤).

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best 0
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— / WHY IT WORKS

The idea underneath.

Undo the ×/÷

Divide both sides by the positive coefficient of x.

Why it works

Scaling both sides equally keeps the order.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve for x: 3x < -12

1

The inequality

Solve for x just like an equation — with one twist. 3x < -12

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x < -4

EX 2medium

Solve for x: 3x ≥ -18

1

The inequality

Solve for x just like an equation — with one twist. 3x ≥ -18

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x ≥ -6

EX 3hard

Solve for x: 3x ≤ -15

1

The inequality

Solve for x just like an equation — with one twist. 3x ≤ -15

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x ≤ -5

04 / COMMON TRAPS

Where students slip.

Trap

Flipping after dividing by a positive.

Fix

Only a NEGATIVE divisor flips the sign.

Trap

Dividing only one side.

Fix

Do the same to both sides.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Solve for x: 2x < -8

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
C2

Solve for x: 5x ≥ 20

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
C3

Solve for x: 4x ≥ 20

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
C4

Solve for x: 4x ≤ -24

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
Apply

Apply (4)

A1

Solve for x: 3x < 6

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
A2

Solve for x: 4x > 16

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
A3

Solve for x: 2x < 2

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
A4

Solve for x: 4x ≥ -16

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
Extension

Extension (4)

E1

Solve for x: 5x < 10

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
E2

Solve for x: 4x ≤ -24

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
E3

Solve for x: 4x < -4

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.
E4

Solve for x: 5x ≤ -25

Need a hint?
  • Divide both sides by the coefficient.
  • Positive divisor → keep the sign.