Solving Equations & Literal Equations — Practice
Every step you take must keep the two sides equal. Say which property justifies it, and the algebra never drifts.
What these questions cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
Problem 1
Solve 5x - 8 = 27.
Worked answer
7
5x = 35
x = 7
Problem 2
Solve 3(x + 2) = 21.
Worked answer
5
3x + 6 = 21
3x = 15
x = 5
Problem 3
Solve 6x + 1 = 4x + 13.
Worked answer
6
2x + 1 = 13
2x = 12
x = 6
Problem 4
Solve y = mx for x.
Worked answer
y/m
x = ym
Problem 5
Solve A = lw for w.
Worked answer
A/l
w = Al
Problem 6
Solve x3 + x6 = 5.
Worked answer
10
2x + x = 30
3x = 30
x = 10
Problem 7
Solve 3x - 14 = x + 52.
Worked answer
11
3x - 1 = 2(x + 5)
3x - 1 = 2x + 10
x = 11
Problem 8
Solve y = mx + b for x.
Worked answer
(y - b)/m
y - b = mx
x = y - bm
Problem 9
Solve C = 59(F - 32) for F.
Worked answer
9C/5 + 32
9C5 = F - 32
F = 9C5 + 32
Problem 10
Solve 4(x - 2) = 4x - 8. If every value works, answer "all".
Worked answer
all
4x - 8 = 4x - 8
Identical, so every value works
Problem 11
Solve 5x + 3 = 5x - 2. If there is no solution, answer "none".
Worked answer
none
Subtract 5x: 3 = -2
False, so no solution
Problem 12
Solve 2(3x - 4) = 5(x + 1).
Worked answer
13
6x - 8 = 5x + 5
x = 13
Problem 13
Solve A = 12bh for h.
Worked answer
2A/b
2A = bh
h = 2Ab
Problem 14
Solve 2x5 - 3 = x2.
Worked answer
-30
4x - 30 = 5x
-30 = x
x = -30
Problem 15
Solve V = π r2 h for h.
Worked answer
V/(pi r^2)
h = Vπ r2
Problem 16
The perimeter of a rectangle is 58 cm and the length is 4 cm more than the width. Find the width.
Worked answer
12.5
2w + 2(w + 4) = 58
4w + 8 = 58
4w = 50, so w = 12.5 cm