Question

1/3 |2x+3|-1 is less than or equal to 8

Answer 1

`(1)/(3)|2x+3|-1\leq8`

Adding 1 to both sides gives

`(1)/(3)|2x+3|\leq9`

and then multiplying both sides by 3 gives

`|2x+3|\leq27`

At this point, this absolute value inequality can be decomposed into two separate inequalities

`\begin{gathered} -(2x+3)<27 \\ (2x+3)<27 \end{gathered}`

We first solve the first inequality.

Multiplying both sides by -1 reverses the sign of the inequality and gives

`2x+3>-27`

subtracting -3 from both sides we get

`2x>-30`

and finally dividing both sides by 2 gives

`x>-15.`

That is the first solution, the second solution is given by the second inequality 2x+ 3 <27.

Subtracting 3 from both sides and then dividing the equation by 2 gives

`x<12`

Hence, the solution to our inequality is

[tex]-15