Solving Equations · Two-step equations · 3.4

Two-step with negatives.

Two-step equations work the same with negatives — just track the signs carefully. −2x + 7 = 1 → −7 → −2x = −6 → ÷(−2) → x = 3.

01 / THE IDEA

See it work.

Watch the method

Two-step with negatives

−2x + 7 = 1 → −2x = −6 → x = 3.

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−2x+7=1-2x + 7 = 1
1

The equation

Solve for x — find the value that makes both sides equal.

−2x+7=1-2x + 7 = 1
2

Move the constant

Subtract 7 from both sides.

−2x=−6-2x = -6
3

Divide by the coefficient

Divide both sides by -2 to get x by itself.

x=3x = 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

Type the value of x — a number or a fraction like 3/2.

streak 0
best 0
…x =
— / WHY IT WORKS

The idea underneath.

Signs matter

Dividing by a negative coefficient flips the sign of the other side — keep the signs straight.

Why it works

−6 ÷ −2 = 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 4x + 2 = 6

1

The equation

Solve for x — find the value that makes both sides equal. 4x + 2 = 6

2

Move the constant

Subtract 2 from both sides. 4x = 4

3

Divide by the coefficient

Divide both sides by 4 to get x by itself. x = 1

EX 2medium

Solve 5x + 8 = 53

1

The equation

Solve for x — find the value that makes both sides equal. 5x + 8 = 53

2

Move the constant

Subtract 8 from both sides. 5x = 45

3

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = 9

EX 3hard

Solve 5x - 8 = -28

1

The equation

Solve for x — find the value that makes both sides equal. 5x - 8 = -28

2

Move the constant

Add 8 to both sides. 5x = -20

3

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = -4

04 / COMMON TRAPS

Where students slip.

Trap

Dropping a negative sign.

Fix

Carry the signs through each step.

Trap

Forgetting to divide by the negative.

Fix

Divide by the full coefficient, sign included.

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 4x + 7 = 15

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
C2

Solve 4x + 3 = -17

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
C3

Solve 6x + 3 = 27

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
C4

Solve 4x - 1 = 11

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
Apply

Apply (4)

A1

Solve 6x + 9 = 63

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
A2

Solve 6x - 2 = -8

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
A3

Solve 5x - 4 = -34

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
A4

Solve 6x - 4 = 32

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
Extension

Extension (4)

E1

Solve 4x + 7 = 43

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
E2

Solve 3x - 3 = 6

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
E3

Solve 4x - 1 = -21

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.
E4

Solve 5x + 9 = -11

Need a hint?
  • Clear the constant first.
  • Divide by the signed coefficient.