Solving Equations · Capstone · C1

Pick the strategy.

The final skill is choosing: distribute brackets, combine like terms, collect variables to one side, then undo with inverse operations in reverse order — and check by substituting.

01 / THE IDEA

See it work.

Watch the method

Pick the strategy

Read the equation, then apply the right moves in order.

1 / 5
2(x+1)=3x−42(x + 1) = 3x - 4
1

The equation

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

2(x+1)=3x−42(x + 1) = 3x - 4
2

Simplify each side

Distribute and combine like terms on each side.

2x+2=3x−42x + 2 = 3x - 4
3

Collect the x terms

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

−x+2=−4-x + 2 = -4
4

Move the constant

Subtract 2 from both sides.

−x=−6-x = -6
5

Divide by the coefficient

Divide both sides by -1 to get x by itself.

x=6x = 6
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 decision

Brackets → distribute. Like terms → combine. x both sides → collect. Then undo +/− and ×/÷ in reverse. Check the answer.

Why it works

Tidy, gather, isolate, verify.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 5(x + 6) = 20

1

The equation

Solve for x — find the value that makes both sides equal. 5(x + 6) = 20

2

Simplify each side

Distribute and combine like terms on each side. 5x + 30 = 20

3

Move the constant

Subtract 30 from both sides. 5x = -10

4

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = -2

EX 2medium

Solve 5(x + 6) = 15

1

The equation

Solve for x — find the value that makes both sides equal. 5(x + 6) = 15

2

Simplify each side

Distribute and combine like terms on each side. 5x + 30 = 15

3

Move the constant

Subtract 30 from both sides. 5x = -15

4

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = -3

EX 3hard

Solve 4x + 9 = -11

1

The equation

Solve for x — find the value that makes both sides equal. 4x + 9 = -11

2

Move the constant

Subtract 9 from both sides. 4x = -20

3

Divide by the coefficient

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

04 / COMMON TRAPS

Where students slip.

Trap

Skipping straight to dividing.

Fix

Tidy and collect before isolating.

Trap

Not checking the solution.

Fix

Substitute back to confirm.

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 4(x - 6) = -32

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
C2

Solve 6x = 36

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
C3

Solve 3x + 8 = 2x + 3

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
C4

Solve 5x = 15

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
Apply

Apply (4)

A1

Solve 3x = 6

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
A2

Solve 6x + 9 = 15

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
A3

Solve 6x - 4 = 2x + 0

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
A4

Solve 2x = 14

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
Extension

Extension (4)

E1

Solve 6x - 5 = 3x + 19

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
E2

Solve 6x + 3 = 21

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
E3

Solve 5x - 3 = 1x + 1

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.
E4

Solve 4x = 32

Need a hint?
  • Distribute and combine first.
  • Collect x, isolate, then check.