Inequalities · One-step · 2.1

Add or subtract.

You solve an inequality the same way as an equation: undo what’s done to x. Adding or subtracting the same amount from both sides keeps the inequality pointing the same way. x + 3 < 11 → x < 8.

01 / THE IDEA

See it work.

Watch the method

Add or subtract

x + 3 < 11 → subtract 3 → x < 8.

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x+3<11x + 3 < 11
1

The inequality

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

x+3<11x + 3 < 11
2

Isolate x

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

x<8x < 8

On the number line

Shade the solutions.

A open circle excludes 8; 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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— / WHY IT WORKS

The idea underneath.

Undo the +/−

Move the constant to the other side; the symbol is unchanged.

Why it works

A fair move to both sides keeps the balance tilted the same way.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve for x: x+1 ≤ -7

1

The inequality

Solve for x just like an equation — with one twist. x + 1 ≤ -7

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x ≤ -8

EX 2medium

Solve for x: x-1 < 4

1

The inequality

Solve for x just like an equation — with one twist. x - 1 < 4

2

Isolate x

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

EX 3hard

Solve for x: x+6 ≥ -7

1

The inequality

Solve for x just like an equation — with one twist. x + 6 ≥ -7

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x ≥ -13

04 / COMMON TRAPS

Where students slip.

Trap

Flipping the sign for subtraction.

Fix

Only ×/÷ by a negative flips it — not +/−.

Trap

Moving the wrong term.

Fix

Undo the constant attached to x.

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: x+3 > 8

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
C2

Solve for x: x-7 ≥ -5

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
C3

Solve for x: x+9 < 5

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
C4

Solve for x: x-2 ≥ -7

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
Apply

Apply (4)

A1

Solve for x: x+1 > -7

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
A2

Solve for x: x+1 > 9

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
A3

Solve for x: x-1 ≥ 6

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
A4

Solve for x: x+7 ≤ -6

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
Extension

Extension (4)

E1

Solve for x: x-4 < 5

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
E2

Solve for x: x-3 > 2

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
E3

Solve for x: x-1 ≤ 9

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.
E4

Solve for x: x-2 ≤ -9

Need a hint?
  • Subtract (or add) to isolate x.
  • Keep the symbol the same.