Solving Equations — Practice
Undo what was done, in reverse order, doing the same thing to both sides every time.
What these questions cover
These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
- Parallel — Same slope, different intercept.
Problem 1
Solve x + 7 = 19.
Worked answer
12
x = 19 - 7 = 12
Problem 2
Solve 5x = 45.
Worked answer
9
x = 45 ÷ 5 = 9
Problem 3
Solve x4 = 7.
Worked answer
28
x = 7 × 4 = 28
Problem 4
Solve 3x + 2 = 17.
Worked answer
5
3x = 15
x = 5
Problem 5
Solve x - 8 = -3.
Worked answer
5
x = -3 + 8 = 5
Problem 6
Solve 4x - 9 = 23.
Worked answer
8
4x = 32
x = 8
Problem 7
Solve 7x - 4 = 2x + 21.
Worked answer
5
5x - 4 = 21
5x = 25
x = 5
Check: 31 = 31 ✓
Problem 8
Solve 2(x + 3) = 14.
Worked answer
4
2x + 6 = 14
2x = 8
x = 4
Problem 9
Solve 5 - 2x = 17.
Worked answer
-6
-2x = 12
x = -6
Check: 5 - 2(-6) = 5 + 12 = 17 ✓
Problem 10
Solve 3(2x - 1) = 21.
Worked answer
4
2x - 1 = 7
2x = 8
x = 4
Problem 11
Solve x3 + 5 = 9.
Worked answer
12
x3 = 4
x = 12
Problem 12
Solve 6x + 8 = 4x - 10.
Worked answer
-9
2x + 8 = -10
2x = -18
x = -9
Problem 13
Solve 2x3 - 1 = x2 + 4.
Worked answer
30
× 6: 4x - 6 = 3x + 24
x - 6 = 24
x = 30
Check: 20 - 1 = 19 and 15 + 4 = 19 ✓
Problem 14
Solve 5(x - 2) = 3(x + 4).
Worked answer
11
5x - 10 = 3x + 12
2x - 10 = 12
2x = 22
x = 11
Problem 15
Solve 2x + 3 = 2x + 7.
- x = 2
- x = 4
- No solution
- Every number works
Worked answer
No solution
Subtract 2x: 3 = 7
That is false no matter what x is
So there is no solution. The two sides are parallel lines that never meet.
Problem 16
A taxi charges $3.50 plus $2.25 per mile. A ride cost $23.75. How many miles?
Worked answer
9
2.25m = 23.75 - 3.50 = 20.25
m = 20.25 ÷ 2.25 = 9 miles