Question

Which of the following is an equivalent form of the compound inequality
`- 44 \ \textgreater \ - 2x- 8 ⩾ -8` the options are below in picture

Answer 1

Given the compound inequality:

`-44>-2x-8⩾-8`

Let's find the equivalent form of the inequality.

To find the equivalent form, let's simplify the inequality.

SInce it is a compund inequality, we are to seperate the inequalities.

Simplify the first two inequalities, then simplify the last two inequalities.

We have:

First two inequalities: -44 > -2x - 8

Last two inequalities: -2x - 8 ⩾ -8

Let's simplify both

`\begin{gathered} -44>-2x-8 \\ \\ Rewrite\text{ the inequality and change the inequality sign:} \\ -2x-8<-44 \end{gathered}`
`\begin{gathered} \text{Second inequality:} \\ -2x-8⩾-8 \\ \end{gathered}`

Therefore, the equivalent form is:

`-2x-8<-44\text{ and -2x - 8 }⩾\text{ -8}`

ANSWER:

`d.\text{ -2x - 8<-44 and -2x - 8 }⩾\text{ -8}`