Solve linear inequalities in one unknown

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Solve the inequality −5x + 8 > 43.

Remember: Dividing both sides by a negative number reverses the inequality sign.

Move the constant term: −5x > 43 − 8, so −5x > 35.
Divide both sides by (−5). The divisor is negative, so the sign reverses.
The solution is x < −7.

Common mistakes

The sign of the boundary value is wrong. Check the step that moves the constant.
Reversed the sign when dividing by a positive number. It only reverses for a negative number.
Divided by a negative number and kept the sign. Multiplying or dividing by a negative number reverses the inequality.