Question

How do you solve the two step inequality `4x – 6 > 6x – 20`?

Answer 1

Given
`color(white)("XXX")4x-6 > 6x -20`

Subtract `4x` from both sides:
`color(white)("XXX")-6 > 2x-20`

Add `20` to both sides
`color(white)("XXX")14 > 2x`

Divide both sides by `2`
`color(white)("XXX")7 > x`

(If desired) reverse to a more standard form:
`color(white)("XXX")x < 7`

Rules used which relate to evaluating inequalities:
1. The validity and orientation of an inequality is maintained if you
`color(white)("XXX")`- add or subtract the same amount to both sides.
`color(white)("XXX")`-multiply or divide both sides by an amount greater than zero.
2. `(a > b) <=> (b < a)`