Q47. - Algebra 1

Question

Write an equation involving absolute value for each graph.

Step-by-Step Solution

Answer

The absolute value equation will be $\left|x\right|=1.5$.

Step-1. Define absolute value equation.

For any real numbers a and b, if $\left|a\right|=b$ and $b\ge 0$, then $a=b$ or $a=-b$.

Step-2. Find the mid-point of points -1.5 and 1.5.

To find the point midway between two points -1.5 and 1.5, add the two values and divide by 2.

$$\begin{gathered} \text{Midpoint}=\frac{-1.5+1.5}{2} \\ =\frac{0}{2} \\ =0 \end{gathered}$$

Step-3. Write the equation.

Since, the midpoint of -1.5 and 1.5 is 0, that is, the distance from -1.5 to 0 is 1.5 units and the distance from 0 to 1.5 is also 1.5 units.

So, the absolute value equation will be:

$\begin{array}{c}\left|x-0\right|=1.5\\ \left|x\right|=1.5\end{array}$