Multi-Step Equations — Drills
Multi-Step Equations has 6 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 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.
Variables on both sides
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 3 = 2x + 53.
Worked answer
10
5x + 3 = 53
5x = 50
x = 10
Check: both sides give 73 ✓
Problem 2
Solve 6x - 3 = 4x - 17.
Worked answer
-7
2x - 3 = -17
2x = -14
x = -7
Check: both sides give -45 ✓
Bracket
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve -5(x + 8) = -75.
Worked answer
7
-5x - 40 = -75
-5x = -35
x = 7
Problem 2
Solve 4(x + 4) = -4.
Worked answer
-5
4x + 16 = -4
4x = -20
x = -5
Collect
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 5x + 2x + 10 = 66.
Worked answer
8
7x + 10 = 66
7x = 56
x = 8
Problem 2
Solve 4x + 5x + 5 = -58.
Worked answer
-7
9x + 5 = -58
9x = -63
x = -7
Fractions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve x4 + 8 = 7.
Worked answer
-4
x4 = -1
x = 4 × -1
x = -4
Problem 2
Solve x5 - 1 = -6.
Worked answer
-25
x5 = -5
x = 5 × -5
x = -25
Special cases
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7(x + 6) = 7x + 42. Answer "all" if every value works, or "none" if there is no solution.
Worked answer
all
7x + 42 = 7x + 42
Subtract 7x: 42 = 42
True, so every value works.
Problem 2
Solve 2(x + 5) = 2x + 15. Answer "all" if every value works, or "none" if there is no solution.
Worked answer
none
2x + 10 = 2x + 15
Subtract 2x: 10 = 15
False, so there is no solution.
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A service charges $54 plus $11 per mile. The bill was $109. How many miles?
Worked answer
5
11n = 55
n = 5
5 miles
Problem 2
A service charges $15 plus $9 per mile. The bill was $105. How many miles?
Worked answer
10
9n = 90
n = 10
10 miles