# Solving less than or greater than expressions (two-part inequalities)

If there is a `<`, `>`, `<=` or `>=` in the equation then you:

**Examples **

1. Solve the inequality `4x-7<13`

Add 7 to both sides to get `x` on its own.

`4x-7+7<13+7`

`4x<20`

Divide both sides by 4

`(4x)/4<20/4`

`x<5`

2. Solve the inequality `7y\ – 34 ≤ 8`

Add 34 to both sides to get `y` on its own.

`7y-34+34<=8+34`

`7y<=42`

Divide both sides by 7.

`(7y)/7<=(42)/7`

`y<=6`

3. Solve the inequality `3(2y + 1) > 10`

First multiply out the brackets and aim to get `y` on its own.

`3xx2y+3xx1>10`

`6y+3>10`

Subtract 3 from both sides.

`6y+3\ –3>10-3`

`6y > 7`

Divide both sides by 6

`(6y)/6 > 7/6`

`y > 7/6`

`y > 1\1/6`

# Solving less than or greater than expressions (two-part inequalities)

If there is a `<`, `>`, `<=` or `>=` in the equation then you:

**Examples **

1. Solve the inequality `4x-7<13`

Add 7 to both sides to get `x` on its own.

`4x-7+7<13+7`

`4x<20`

Divide both sides by 4

`(4x)/4<20/4`

`x<5`

2. Solve the inequality `7y\ – 34 ≤ 8`

Add 34 to both sides to get `y` on its own.

`7y-34+34<=8+34`

`7y<=42`

Divide both sides by 7.

`(7y)/7<=(42)/7`

`y<=6`

3. Solve the inequality `3(2y + 1) > 10`

First multiply out the brackets and aim to get `y` on its own.

`3xx2y+3xx1>10`

`6y+3>10`

Subtract 3 from both sides.

`6y+3\ –3>10-3`

`6y > 7`

Divide both sides by 6

`(6y)/6 > 7/6`

`y > 7/6`

`y > 1\1/6`