Question

How do you solve -9 < 4x + 3 < 11?

Answer 1

`-3 < x < 2`

Explanation:

Given
`color(white)("XXXX")-9 < 4x + 3 < 11`

Things you can do with expressions in an inequality which maintain the inequality:

• Add the same amount to each expression
• Subtract the same amount from each expression
• Divide each expression by the same amount provided the amount is greater than zero
• Multiply each expression by the same amount provided the amount is greater than zero

So, we can subtract `3` from each expression, to get:
`color(white)("XXXX")-12 < 4x < 8`

Then we can divide each expression by `4`, to get:
`color(white)("XXXX")-3 < x < 2`