Question

What is the solution to the inequality `2 <2(x+4)<18`?

Answer 1

`-3 < x < 5`

Explanation:

Given
`color(white)("XXXX")2 < 2(x+4) < 18`
`rArrcolor(white)("XXXXXXXXXXXXXXX") 2 < 2x+8 <18`

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

`2 < 2(x+4) < 18color(white)("XXX")rArrcolor(white)("XXX") 2 < 2x+8 <18`

Given the above rules, we can subtract `8` from each expression, to get:
`color(white)("XXXX")-6 < 2x < 10`

Then we can divide each expression by `2`, to get:
`color(white)("XXXX")-3 < x < 5`