Solving inequalities, step by step

An inequality is solved almost exactly like an equation.

The question

x + 8 ≤ 20

20−8=12

≤

x≤12

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.
8 was added last, so it comes off first — off BOTH sides: 20 − 8 = 12.
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 ≤ 12. 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.

How it works.

01
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.
02
8 was added last, so it comes off first — off BOTH sides: 20 − 8 = 12.
03
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.
04
So x ≤ 12. 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.