Solving Equations · Apply · 6.1

Translate to an equation.

Word problems become equations: let x be the unknown, turn the words into operations, then solve. “A number times 2, plus 3, is 11” → 2x + 3 = 11 → x = 4.

01 / THE IDEA

See it work.

Watch the method

Translate to an equation

“Twice a number plus 3 is 11” → 2x + 3 = 11.

1 / 3
2x+3=112x + 3 = 11
1

The equation

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

2x+3=112x + 3 = 11
2

Move the constant

Subtract 3 from both sides.

2x=82x = 8
3

Divide by the coefficient

Divide both sides by 2 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.

Words to symbols

Let x stand for the unknown; “times” is ×, “more than” is +, “is” is =. Build the equation, then solve.

Why it works

“3 more than twice x is 11” → 2x + 3 = 11.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A number is multiplied by 4, then 6 is subtracted; the result is -26. What is the number?

1

The equation

Solve for x — find the value that makes both sides equal. 4x - 6 = -26

2

Move the constant

Add 6 to both sides. 4x = -20

3

Divide by the coefficient

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

EX 2medium

A number is multiplied by 6, then 9 is added; the result is -3. What is the number?

1

The equation

Solve for x — find the value that makes both sides equal. 6x + 9 = -3

2

Move the constant

Subtract 9 from both sides. 6x = -12

3

Divide by the coefficient

Divide both sides by 6 to get x by itself. x = -2

EX 3hard

A number is multiplied by 6, then 9 is added; the result is -21. What is the number?

1

The equation

Solve for x — find the value that makes both sides equal. 6x + 9 = -21

2

Move the constant

Subtract 9 from both sides. 6x = -30

3

Divide by the coefficient

Divide both sides by 6 to get x by itself. x = -5

04 / COMMON TRAPS

Where students slip.

Trap

Mis-ordering the operations.

Fix

Translate the phrase carefully, left to right.

Trap

Forgetting to define x.

Fix

Say what x represents first.

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

A number is multiplied by 3, then 3 is subtracted; the result is 3. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
C2

A number is multiplied by 5, then 9 is added; the result is 24. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
C3

A number is multiplied by 4, then 2 is subtracted; the result is -10. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
C4

A number is multiplied by 4, then 1 is subtracted; the result is -21. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
Apply

Apply (4)

A1

A number is multiplied by 5, then 4 is added; the result is -11. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
A2

A number is multiplied by 5, then 7 is added; the result is -3. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
A3

A number is multiplied by 5, then 8 is added; the result is -12. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
A4

A number is multiplied by 5, then 4 is subtracted; the result is 11. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
Extension

Extension (4)

E1

A number is multiplied by 6, then 7 is added; the result is -17. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
E2

A number is multiplied by 2, then 3 is subtracted; the result is -5. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
E3

A number is multiplied by 5, then 9 is added; the result is 44. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.
E4

A number is multiplied by 4, then 9 is subtracted; the result is -1. What is the number?

Need a hint?
  • Let x be the unknown number.
  • Turn each phrase into an operation.