Question

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

Answer 1

Answer:

[-6,-3]

Step-by-step 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 :)