Question

How do you solve the inequality `8 − 2x < 4`?

Answer 1

`x > 2`

Explanation:

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

• 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

Things you can do with expressions in an inequality which reverse the inequality orientation.

• Divide each expression by the same amount when the amount is less than zero
• Multiply each expression by the same amount when the amount is less than zero

Given the above rules:

`color(white)("XXXX")8-2x < 4`
subtract `8` from both sides:
`color(white)("XXXX")-2x < -4`
divide both sides by `(-2)`, which reverses orientation of inequality
`color(white)("XXXX")x > 2`