Linear Inequalities — Drills
Linear Inequalities 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.
- Inequality — A statement that one expression is less than or greater than another.
- Open — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 10 > 24.
Worked answer
x > 2
7x > 14
x > 2
Problem 2
Solve 6x - 2 ≤ 46.
Worked answer
x <= 8
6x ≤ 48
x ≤ 8
Flip
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve -6x - 7 ≥ -49.
Worked answer
x <= 7
-6x ≥ -42
Divide by -6 and flip: x ≤ 7
Problem 2
Solve -5x + 6 < 41.
Worked answer
x > -7
-5x < 35
Divide by -5 and flip: x > -7
Circle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For the solution x ≥ 2, is the circle at 2 open or filled?
Worked answer
filled
x = 2 is a solution.
So the circle is filled.
Problem 2
For the solution x ≥ 0, is the circle at 0 open or filled?
Worked answer
filled
x = 0 is a solution.
So the circle is filled.
Compound
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve -9 ≤ 4x - 1 < 23.
Worked answer
-2 <= x < 6
Subtract -1: -8 ≤ 4x < 24
Divide by 4: -2 ≤ x < 6
Problem 2
Solve -25 ≤ 5x - 5 < 0.
Worked answer
-4 <= x < 1
Subtract -5: -20 ≤ 5x < 5
Divide by 5: -4 ≤ x < 1
Words
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
"More than 35" translates to
- x < 35
- x ≥ 35
- x > 35
- x ≤ 35
Worked answer
x > 35
"More than" means strictly greater.
So x > 35.
Problem 2
"Fewer than 28" translates to
- x < 28
- x ≤ 28
- x ≥ 28
- x > 28
Worked answer
x < 28
"Fewer than" means strictly less.
So x < 28.
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Entry costs $27 and each song is $7. With $73, how many songs can you afford?
Worked answer
6
7n ≤ 46
n ≤ 6.57
Whole songs only, so 6.
Problem 2
Entry costs $7 and each game is $6. With $81, how many games can you afford?
Worked answer
12
6n ≤ 74
n ≤ 12.33
Whole games only, so 12.
Variables on both sides
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 7x + 2 ≤ 2x + 47.
Worked answer
x <= 9
5x + 2 ≤ 47
5x ≤ 45
x ≤ 9
Problem 2
Solve 6x - 2 > 4x - 14.
Worked answer
x > -6
2x - 2 > -14
2x > -12
x > -6