Q5. - Algebra 1

Question

Which absolute value equation has the graph below as its solution?

A $\left|x-3\right|\mathbf{=}\mathbf{11}$

B  $\left|x-4\right|\mathbf{=}\mathbf{12}$

C $\left|x-11\right|\mathbf{=}\mathbf{3}$

D $\left|x-12\right|\mathbf{=}\mathbf{4}$

Step-by-Step Solution

Answer

The correct option is represented by C.

Step 1. Check whether the first option is the required option or not.

The provided graph indicates two points which are positive represented by 8 and 14. Perform substitution of these values into the left side of the first option.

$\left|8-3\right|=5$

As the obtain value is not 11 so this option is incorrect.

Step 2. Check whether the second option is the required option or not.

Perform substitution of the provided values into the left side of the second option.

$\left|8-4\right|=4$

As the obtain value is not 12 so this option is incorrect.

Step 3. Check whether the third option is the required option or not.

Perform substitution of provided values into the left side of the third option.

$\left|8-11\right|=3$

As the obtain value is 3 so this option is correct.

Step 4. Check whether the fourth option is the required option or not.

Perform substitution of the provided values into the left side of the fourth option.

$\left|8-12\right|=4$

$\left|14-12\right|=2$

As the second obtain value is not 4 so this option is incorrect.