Recognise the pattern
Per-item amount × quantity, plus or minus a fixed amount, equals a total.
Why it works
rate × x ± fixed = total.
Solving Equations · Apply · 6.3
Number & money problems.
Many problems fit ax ± b = c: a price each, a fee, a total; a number scaled and shifted. Identify the structure and solve. “5 tickets plus a $3 fee cost $18” → 5x + 3 = 18.
See it work.
Watch the method
Number & money problems
“5 of something plus 3 is 18” → 5x + 3 = 18.
1
The equation
Solve for x — find the value that makes both sides equal.
2
Move the constant
Add 3 to both sides.
3
Divide by the coefficient
Divide both sides by 5 to get x by itself.
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 =
The idea underneath.
From easy to tricky.
A number is multiplied by 2, then 6 is subtracted; the result is 0. What is the number?
1
The equation
Solve for x — find the value that makes both sides equal. 2x - 6 = 0
2
Move the constant
Add 6 to both sides. 2x = 6
3
Divide by the coefficient
Divide both sides by 2 to get x by itself. x = 3
A number is multiplied by 5, then 1 is added; the result is 21. What is the number?
1
The equation
Solve for x — find the value that makes both sides equal. 5x + 1 = 21
2
Move the constant
Subtract 1 from both sides. 5x = 20
3
Divide by the coefficient
Divide both sides by 5 to get x by itself. x = 4
A number is multiplied by 6, then 2 is added; the result is -22. What is the number?
1
The equation
Solve for x — find the value that makes both sides equal. 6x + 2 = -22
2
Move the constant
Subtract 2 from both sides. 6x = -24
3
Divide by the coefficient
Divide both sides by 6 to get x by itself. x = -4
Where students slip.
Trap
Mixing the rate and the fixed amount.
Fix
The per-item amount multiplies x; the fee is added.
Trap
Wrong operation for the fee.
Fix
Read whether it’s added or taken off.
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 4, then 8 is subtracted; the result is 28. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
C2
A number is multiplied by 2, then 9 is added; the result is 17. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
C3
A number is multiplied by 5, then 5 is added; the result is 25. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
C4
A number is multiplied by 6, then 2 is subtracted; the result is 22. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
Apply
Apply (4)
A1
A number is multiplied by 2, then 9 is subtracted; the result is -7. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
A2
A number is multiplied by 6, then 8 is subtracted; the result is 22. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
A3
A number is multiplied by 3, then 8 is subtracted; the result is -26. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
A4
A number is multiplied by 6, then 9 is subtracted; the result is -3. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
Extension
Extension (4)
E1
A number is multiplied by 4, then 4 is added; the result is 28. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
E2
A number is multiplied by 3, then 1 is added; the result is -2. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
E3
A number is multiplied by 6, then 5 is added; the result is -1. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.
E4
A number is multiplied by 4, then 3 is added; the result is 31. What is the number?
Need a hint?
- Find the rate (coefficient) and the fixed amount.
- Write ax ± b = c and solve.