Two-step inequalities

The question

−6x + 2 ≥ 38

38−2=36

36÷−6=−6

≥→≤

x≤−6

Solve an inequality like an equation — the same moves on both sides. There is one extra rule at the end.
2 was added last, so it comes off first — from both sides: 38 − 2 = 36.
Now divide both sides by −6: 36 ÷ −6 = −6.
Here is the extra rule: dividing both sides by a negative turns the sign round, so ≥ becomes ≤.
So x ≤ −6. That is a whole range of numbers, not just one.

How it works.

01
Solve an inequality like an equation — the same moves on both sides. There is one extra rule at the end.
02
2 was added last, so it comes off first — from both sides: 38 − 2 = 36.
03
Now divide both sides by −6: 36 ÷ −6 = −6.
04
Here is the extra rule: dividing both sides by a negative turns the sign round, so ≥ becomes ≤.
05
So x ≤ −6. That is a whole range of numbers, not just one.