Inequalities · One-step · 2.4

One-step mastery.

Mixed one-step practice: decide whether the last operation on x is +/− (never flip) or ×/÷ (flip only if the number is negative), undo it, and write the solution.

01 / THE IDEA

See it work.

Watch the method

One-step mastery

Undo one operation; flip only for ×/÷ by a negative.

1 / 2
−4x≥12-4x \ge 12
1

The inequality

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

−4x≥12-4x \ge 12
2

Flip the sign!

Dividing both sides by the negative -4 reverses the inequality.

x≤−3x ≤ -3

On the number line

Shade the solutions.

A closed circle includes -3; the arrow points to every value that works.

-8-7-6-5-4-3-2-1012
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

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

streak 0
best 0
…
— / WHY IT WORKS

The idea underneath.

Pick the move

Identify the single operation tying up x and reverse it, watching for the flip case.

Why it works

Ask: is the coefficient negative?

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve for x: -3x < -6

1

The inequality

Solve for x just like an equation — with one twist. -3x < -6

2

Flip the sign!

Dividing both sides by the negative -3 reverses the inequality. x > 2

EX 2medium

Solve for x: x-4 > 6

1

The inequality

Solve for x just like an equation — with one twist. x - 4 > 6

2

Isolate x

Undo the operations to get x alone (the sign stays the same). x > 10

EX 3hard

Solve for x: 6x ≤ 24

1

The inequality

Solve for x just like an equation — with one twist. 6x ≤ 24

2

Isolate x

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

04 / COMMON TRAPS

Where students slip.

Trap

Flipping every time.

Fix

Only ×/÷ by a negative flips.

Trap

Never flipping.

Fix

A negative coefficient demands the flip.

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: 6x ≤ 36

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
C2

Solve for x: x-4 > 1

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
C3

Solve for x: x+8 < 7

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
C4

Solve for x: 2x < -10

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
Apply

Apply (4)

A1

Solve for x: 4x ≤ 8

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
A2

Solve for x: 3x ≥ -12

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
A3

Solve for x: -3x < 3

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
A4

Solve for x: -2x < -2

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
Extension

Extension (4)

E1

Solve for x: 4x ≤ 16

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
E2

Solve for x: -4x ≤ 16

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
E3

Solve for x: 2x > 8

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.
E4

Solve for x: -6x > 24

Need a hint?
  • Find the one operation on x.
  • Flip only if dividing by a negative.