Question

HELP! i’m confused! question is in the picture

Answer 1

[-6,-3]

Explanation:

So we have the compound inequality:

`2x+7\leq x+4\leq 3x+16`

Let's solve for each of the inequalities:

1)

We have:

`2x+7\leq x+4`

Subtract x from both sides:

`x+7\leq 4`

Subtract 7 from both sides:

`x\leq -3`

So that's one of our answers.

2)

We have:

`x+4\leq 3x+16`

Subtract 3x from both sides:

`-2x+4\leq 16`

Subtract 4 from both sides:

`-2x\leq 12`

Divide both sides by -2. Since we're dividing by a negative, flip the sign:

`x\geq -6`

Therefore, our entire answer is:

`-6\leq x\leq -3`

This means all values in between -3 and -6 including -3 and -6.

In interval notation, this is:

`[-6,-3]`

So, A is -6.

And B is -3.

And we're done :)