InequalitiesTo 50
Name: Date:
Solve each one, then write >, <, ≥ or ≤ in the box.
14x + 2 ≥ 34x8
25x + 12 ≥ 2x−2
3−6x + 12 < 0x2
43x + 12 > −33x−15
5−4x + 8 ≤ −4x3
62x + 7 ≥ −41x−24
7−5x + 9 > 19x−2
8−8x + 8 < −32x5
Two-step inequalities worksheets
A two-step inequality is undone in two moves, in reverse order — and if either move divides by a negative, the sign flips. These free printable worksheets practice both steps together.
Kid stuck on one? You don’t just get the sheet.
Two-step inequalities
The answer key prints on a separate page.
What's on this sheet
2x + 3 ≤ 11 comes apart the way its equation does: subtract the 3, then divide by the 2, giving x ≤ 4. The order matters — the adding is undone first, the multiplying second — and it is the same reverse order the two-step equation page teaches, now with a direction to keep track of as well.
Why this sheet works
When the division step uses a negative, the sign turns over, so these sheets carry both kinds and the answer always names the direction. A right number with a wrong sign is marked wrong, which is what makes the flip stick. This is the step up from the one-step inequality pages — the number line at the end is the same, but there are two operations to unwind before it can be drawn.
How this one works
One question from this sheet, worked through a step at a time.
4x + 2 ≥ 34
4x + 2 ≥ 34
34−2=32
32÷4=8
≥
x≥8
- An inequality comes apart exactly like an equation — the same moves, done to both sides. There is one extra rule and it arrives at the end, so start by ignoring the sign and solving for x.
- 2 was added last, so it comes off first — off BOTH sides: 34 − 2 = 32.
- Now divide both sides by 4: 32 ÷ 4 = 8.
- Nothing was divided by a negative here, so the sign has not moved: it is still ≥. That is the one thing to check on every one of these before writing the answer down.
- So x ≥ 8. That is a whole RANGE of numbers rather than one, which is what makes this different from an equation — and why the sign is half the answer.