Multi-Step Equations — Challenge
Distribute, collect, then undo. Every linear equation, however long, yields to that order.
What these problems cover
These questions use 4 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Multiplier — The single number you multiply by. A 20% increase has multiplier 1.20.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- Like terms — Terms with exactly the same variable part; only these can be combined.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
Problem 1
Solve 2x+5=17.
- 5
- 6
- 7
- 11
- 22
Worked answer
6
Undo the addition first: 2x = 17-5 = 12.
Then undo the multiplication: x = 122 = 6.
Check: 2(6)+5 = 17.
Problem 2
Solve 3(x-2)=18.
- 4
- 6
- 8
- 20
- 54
Worked answer
8
Divide both sides by 3: x-2 = 6.
Add 2: x = 8.
Check: 3(8-2) = 3· 6 = 18.
Problem 3
Solve 5x-3=2x+12.
- 3
- 4
- 5
- 9
- 15
Worked answer
5
Collect the x terms on the left: subtract 2x from both sides to get 3x-3 = 12.
Add 3: 3x = 15, so x = 5.
Check: 5(5)-3 = 22 and 2(5)+12 = 22.
Problem 4
Solve 2x+13=5.
- 5
- 7
- 8
- 14
- 16
Worked answer
7
Multiply both sides by 3 to clear the fraction: 2x+1 = 15.
Subtract 1: 2x = 14, so x = 7.
Check: 2(7)+13 = 153 = 5.
Problem 5
Solve 4x=36.
- 6
- 8
- 9
- 32
- 144
Worked answer
9
Divide both sides by 4.
x = 364 = 9.
Check: 4(9) = 36.
Problem 6
Solve 7-2x=1.
- 2
- 3
- 4
- -3
- 8
Worked answer
3
Subtract 7 from both sides: -2x = -6.
Divide by -2: x = 3. A negative divided by a negative is positive.
Check: 7-2(3) = 1.
Problem 7
Solve 4(x+3)-2x=20.
- 2
- 3
- 4
- 5
- 8
Worked answer
4
Expand the bracket: 4x+12-2x = 20.
Collect like terms: 2x+12 = 20, so 2x = 8 and x = 4.
Check: 4(7)-8 = 28-8 = 20.
Problem 8
Solve x4+2=6.
- 8
- 12
- 16
- 24
- 32
Worked answer
16
Subtract 2 from both sides: x4 = 4.
Multiply by 4: x = 16.
Check: 164+2 = 4+2 = 6.