Multi-Step Equations — Practice
Distribute, collect, then undo. Every linear equation, however long, yields to that order.
What these questions 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 4x + 3 = 2x + 11.
Worked answer
4
2x + 3 = 11
2x = 8
x = 4
Problem 2
Solve 7y - 5 = 3y + 15.
Worked answer
5
4y - 5 = 15
4y = 20
y = 5
Problem 3
Solve 3(x + 4) = 27.
Worked answer
5
3x + 12 = 27
3x = 15
x = 5
Problem 4
Solve 2(n - 7) = 10.
Worked answer
12
2n - 14 = 10
2n = 24
n = 12
Problem 5
Solve 5x + 2x - 6 = 22.
Worked answer
4
7x - 6 = 22
7x = 28
x = 4
Problem 6
Solve 5(2x - 3) = 3(x + 6).
Worked answer
33/7
10x - 15 = 3x + 18
7x = 33
x = 337
Problem 7
Solve 9 - 4x = 2x - 15.
Worked answer
4
9 = 6x - 15
24 = 6x
x = 4
Problem 8
Solve -3(x - 5) = 21.
Worked answer
-2
-3x + 15 = 21
-3x = 6
x = -2
Problem 9
Solve x4 + 3 = 10.
Worked answer
28
x4 = 7
x = 28
Problem 10
Solve 2x + 15 = 3.
Worked answer
7
2x + 1 = 15
2x = 14
x = 7
Problem 11
How many solutions does 4(x + 2) = 4x + 8 have?
- Infinitely many
- Exactly one
- None
- Exactly two
Worked answer
Infinitely many
4x + 8 = 4x + 8
The two sides are identical
Every value of x works
Problem 12
Solve 2(x + 3) = 2x + 1. If there is no solution, answer "none".
Worked answer
none
2x + 6 = 2x + 1
6 = 1, which is false
So there is no solution
Problem 13
A rental costs $25 plus $7 per hour. The bill was $67. How many hours?
Worked answer
6
7h = 42
h = 6
6 hours
Problem 14
Two numbers differ by 8 and add to 46. Find the larger one.
Worked answer
27
x + (x + 8) = 46
2x = 38, so x = 19
The larger is 27
Problem 15
Solve 6 - 2(3x - 4) = 4x + 9.
Worked answer
1/2
6 - 6x + 8 = 4x + 9
14 - 6x = 4x + 9
5 = 10x
x = 12
Problem 16
A phone plan charges $30 plus $0.05 per text. Another charges $20 plus $0.09 per text. At how many texts do they cost the same?
Worked answer
250
30 + 0.05t = 20 + 0.09t
10 = 0.04t
t = 250 texts