Question

9. Solve the compound inequality 2x>-10 and 3x < 24.-5x<-8-585>x>-8

Answer 1

In this problem, we want to solve two inequalities.

There is one rule that is important to remember with inequalities:

- If you multiply or divide by a negative number in the last step, you must flip the inequality symbols.

We are given:

`2x>-10\text{ and }3x<24`

We can solve these one at a time. Beginning with the first inequality,

`2x>-10`

Divide by 2 on both sides:

`\begin{gathered} (2x)/(x)>(-10)/(2) \\ \\ x>-5 \end{gathered}`

Moving on to the second inequality, we get:

`\begin{gathered} 3x<24 \\ \\ \text{ Divide by 3 on both sides:} \\ \\ (3x)/(3)<(24)/(3) \\ \\ x<8 \end{gathered}`

So now we know that x is greater than -5 but less than 8.

Let's see what that looks like on a numberline:

We see that the values of x can be included within a lower bound and an upper bound at -5 and 8.

This means we can write the final inequality as

[tex]\boxed{-5