Solving Equations · Variables on both sides · 4.4

Both-sides mastery.

Bring it together: collect the variable terms, move the constants, then divide — watching signs throughout. 6x − 5 = 3x + 7 → 3x − 5 = 7 → 3x = 12 → x = 4.

01 / THE IDEA

See it work.

Watch the method

Both-sides mastery

6x − 5 = 3x + 7 → x = 4.

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6x−5=3x+76x - 5 = 3x + 7
1

The equation

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

6x−5=3x+76x - 5 = 3x + 7
2

Collect the x terms

Subtract 3x from both sides to get the x terms together.

3x−5=73x - 5 = 7
3

Move the constant

Add 5 to both sides.

3x=123x = 12
4

Divide by the coefficient

Divide both sides by 3 to get x by itself.

x=4x = 4
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.

The full routine

Variables to one side, constants to the other, then divide by the coefficient.

Why it works

x’s together, numbers together, then split.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 3x - 5 = 2x - 8

1

The equation

Solve for x — find the value that makes both sides equal. 3x - 5 = 2x - 8

2

Collect the x terms

Subtract 2x from both sides to get the x terms together. x - 5 = -8

3

Move the constant

Add 5 to both sides. x = -3

4

Read the solution

x is already by itself. x = -3

EX 2medium

Solve 7x - 1 = 5x + 1

1

The equation

Solve for x — find the value that makes both sides equal. 7x - 1 = 5x + 1

2

Collect the x terms

Subtract 5x from both sides to get the x terms together. 2x - 1 = 1

3

Move the constant

Add 1 to both sides. 2x = 2

4

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = 1

EX 3hard

Solve 3x - 4 = 2x - 9

1

The equation

Solve for x — find the value that makes both sides equal. 3x - 4 = 2x - 9

2

Collect the x terms

Subtract 2x from both sides to get the x terms together. x - 4 = -9

3

Move the constant

Add 4 to both sides. x = -5

4

Read the solution

x is already by itself. x = -5

04 / COMMON TRAPS

Where students slip.

Trap

Mixing the order of moves.

Fix

Variables first, then constants.

Trap

Sign slips with negatives.

Fix

Track every sign.

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 6x - 7 = 4x - 13

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
C2

Solve 7x - 4 = 1x - 22

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
C3

Solve 6x + 4 = 4x + 20

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
C4

Solve 4x - 4 = 1x - 13

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
Apply

Apply (4)

A1

Solve 7x - 4 = 3x - 20

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
A2

Solve 3x + 7 = 2x + 15

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
A3

Solve 5x + 4 = 4x + 12

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
A4

Solve 5x - 4 = 1x + 16

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
Extension

Extension (4)

E1

Solve 6x + 6 = 2x + 34

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
E2

Solve 7x - 2 = 4x + 16

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
E3

Solve 4x - 7 = 1x - 4

Need a hint?
  • Collect x terms.
  • Move constants, then divide.
E4

Solve 5x - 7 = 1x - 15

Need a hint?
  • Collect x terms.
  • Move constants, then divide.