Question

Find the solution set of this inequality. Select

Answer 1

Answer:

"first number line shown in the diagram"

Step-by-step explanation:

Whenever we have inequality of the form

| x + a | > b

we can write

1.  x+a > b, and

2. -(x+a) > b

and solve both.

So we can write

1. 8x + 16 > 16

2. -(8x+16) > 16

Solving 1:

8x > 16 - 16

8x > 0

x > 0

Solving 2:

-(8x+16) > 16

-8x - 16 > 16

-16 -16 > 8x

-32 > 8x

-32/8 > x

-4 > x

Putting these together, we can say x is greater than 0 & x is less than -4

The first number line is right.

Answer 2

Hello!

The answer is:

The first option.

$-4>x>0$

Why?

To solve absolute values inequalities, we need to remember that absolute value functions have a positive and a negative solution.

For example, we have that:

$|x|>1$

The solution will be

$-1>x>1$

So, we are given the inequality:

$|8x+16|>16$

Isolating "x", we have:

$-16>8x+16>16$

$-16-16>8x+16-16>16-16$

$-32>8x>0$

$\frac{-32}{8}>\frac{8x}{32}>\frac{0}{32}\\\\-4>x>0$

Hence, we have that the correct option is the first option.

The solution is:

$-4>x>0$

or

(-∞,-4)U(0,∞)

Have a nice day!