Two-step inequalities, step by step
A two-step inequality is undone in two moves, in reverse order.
−6x + 2 ≥ 38
- 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: 38 − 2 = 36.
- Now divide both sides by −6: 36 ÷ −6 = −6.
- Here is the extra rule, and it is the only one: dividing both sides by a NEGATIVE turns the sign round, so ≥ becomes ≤. Do not take that on trust — put a number from the answer back into the question and see which way it has to face.
- So x ≤ −6. 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
2 was added last, so it comes off first — off BOTH sides: 38 − 2 = 36.
- 03
Now divide both sides by −6: 36 ÷ −6 = −6.
- 04
Here is the extra rule, and it is the only one: dividing both sides by a NEGATIVE turns the sign round, so ≥ becomes ≤. Do not take that on trust — put a number from the answer back into the question and see which way it has to face.
- 05
So x ≤ −6. 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.