Question

Write an absolute value equation for each solution set graphed below.

Short answer

Absolute value equations are

a. $\left|x\right|=4$and b. $\left|x-6\right|=2$

Step-by-step solution

a.Step 1 - Define absolute value

Absolute value of a number is its distance from 0 on the number line.

- Observation from figure

Distance of solution set is 4 units from origin.

- Write absolute value equation

Let x be the distance from origin so required equation is $x=-4\text{or}x=4$which in absolute value form will be written as $\left|x\right|=4$

b.Step 1 - Define absolute value

Absolute value of a number is its distance from 0 on the number line.

- Observation from figure

Distance of solution set is 2 units from a point six.

- Write absolute value equation

Let x be the distance from point 6. To make required equation subtract 6 from x to get $x-6=-2\text{or}x-6=2$which in absolute value form will be written as $\left|x-6\right|=2$