Question

Solve and graph the absolute value inequality: |2x + 4| > 14

number line with open circles on _9 and 5, shading going in the opposite directions.

number line with open circles on _9 and 5, shading in between.

number line with closed circles on _9 and 5, shading going in the opposite directions.

a number line with open circles on _5 and 5, shading going in the opposite directions.

Answer 1

Option (a) is correct.

number line with open circles on -9 and 5, shading going in the opposite directions.

Explanation:

Given : absolute value inequality: |2x + 4| > 14

We have to solve and graph the given absolute value inequality: |2x + 4| > 14

Consider the given absolute value inequality: |2x + 4| > 14

`\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a`

`2x+4<-14\quad \mathrm{or}\quad \:2x+4>14`

Consider first inequality ,

`2x+4<-14`

Subtract 4 both side, we get,

`2x+4-4<-14-4`

Simplify

`2x<-18`

Divide both side by 2, we get,

`(2x)/(2)<(-18)/(2)`

`x<-9\\`

Now, consider the second inequality,

`2x+4>14`

Subtract 4 both side, we get,

`2x+4-4>14-4`

Simplify

`2x>10`

Divide both side by 2, we get,

`(2x)/(2)>(10)/(2)`

`x>5\\`

Thus, we obtain the solution for absolute value inequality: |2x + 4| > 14 as
`\left(-\infty \:,\:-9\right)\cup \left(5,\:\infty \:\right)`

On number line as shown below.

On graph as shown below.

Option (a) is correct.

Thus, number line with open circles on -9 and 5, shading going in the opposite directions.

Answer 2

it is very simple, |2x + 4| > 14, we have 2x+4>14 or -(2x+4) >14 (absolute value definition) so 2x> 14-4, x>10/2=5 or -2x>14+4, -x>18/2=9, implies x< - 9
the solution is x>5, or x< -9, so the answer is number line with open circles on _9 and 5, shading going in the opposite directions.