Solving Equations & Literal Equations — Drills
Solving Equations & Literal 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 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.
Linear
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 2 = -33.
Worked answer
-5
7x = -35
x = -5
Problem 2
Solve 5x - 12 = -12.
Worked answer
0
5x = 0
x = 0
Variables on both sides
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 3 = 2x + 48.
Worked answer
9
5x + 3 = 48
5x = 45
x = 9
Problem 2
Solve 6x - 3 = 4x - 15.
Worked answer
-6
2x - 3 = -15
2x = -12
x = -6
Literal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve d = rt for t.
Worked answer
d/r
Divide both sides by r.
t = dr
Problem 2
Solve P = 2l + 2w for w.
Worked answer
(P - 2l)/2
Subtract 2l: P - 2l = 2w
Divide by 2: w = P - 2l2
Fractions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 5x4 + 3x4 = -96.
Worked answer
-48
× 16: 20x + 12x = -1536
32x = -1536
x = -48
Problem 2
Solve 3x5 + 2x4 = 66.
Worked answer
60
× 20: 12x + 10x = 1320
22x = 1320
x = 60
Special cases
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 8(x + 6) = 8x + 48. Answer "all" if every value works, or "none" if there is none.
Worked answer
all
8x + 48 = 8x + 48
Subtract 8x: 48 = 48
True, so every value works.
Problem 2
Solve 2(x + 5) = 2x + 16. Answer "all" if every value works, or "none" if there is none.
Worked answer
none
2x + 10 = 2x + 16
Subtract 2x: 10 = 16
False, so no solution.
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A rectangle has perimeter 110 cm and its length is 9 cm more than its width. Find the width.
Worked answer
23
2w + 2(w + 9) = 110
4w + 18 = 110
4w = 92
w = 23 cm
Problem 2
A rectangle has perimeter 40 cm and its length is 8 cm more than its width. Find the width.
Worked answer
6
2w + 2(w + 8) = 40
4w + 16 = 40
4w = 24
w = 6 cm