Solving Equations — Drills
Solving Equations has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
One-step
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve x - 13 = 7.
Worked answer
20
x = 7 + 13 = 20
Problem 2
Solve x8 = -12.
Worked answer
-96
x = -12 × 8 = -96
Two-step
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 8x - 6 = 26.
Worked answer
4
8x = 26 + 6 = 32
x = 32 ÷ 8 = 4
Problem 2
Solve 2x + 13 = 13.
Worked answer
0
2x = 13 - 13 = 0
x = 0 ÷ 2 = 0
Bothsides
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 5x + 12 = 3x + 20.
Worked answer
4
2x + 12 = 20
2x = 8
x = 4
Problem 2
Solve 6x + 6 = 3x - 12.
Worked answer
-6
3x + 6 = -12
3x = -18
x = -6
Parens
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 2(4x + 0) = 24.
Worked answer
3
4x + 0 = 12
4x = 12
x = 3
Problem 2
Solve 4(3x - 4) = -76.
Worked answer
-5
3x - 4 = -19
3x = -15
x = -5
Fractions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve x2 + 7 = 15.
Worked answer
16
x2 = 8
x = 8 × 2 = 16
Problem 2
Solve x4 + 5 = 7.
Worked answer
8
x4 = 2
x = 2 × 4 = 8
Special cases
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 6 = 7x + 14.
- Every number works
- No solution
- x = 0
- x = 8
Worked answer
No solution
Subtract 7x: 6 = 14
That is false whatever x is
So there is no solution.
Problem 2
Solve 2(x + 5) = 2x + 10.
- No solution
- Every number works
- x = 5
- x = 0
Worked answer
Every number works
2x + 10 = 2x + 10
Both sides are identical
So every number is a solution.
Wordeq
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A taxi charges $2.50 plus $2.25 per mile. A ride cost $25.00. How many miles?
Worked answer
10
2.25m = 22.50
m = 22.50 ÷ 2.25 = 10 miles
Problem 2
A taxi charges $3.50 plus $2.00 per mile. A ride cost $13.50. How many miles?
Worked answer
5
2.00m = 10.00
m = 10.00 ÷ 2.00 = 5 miles