Target Test Prep Sample Numeric Entry Problem

Solution:

The absolute value bars must first be isolated by adding 5 to both sides of the equation and then dividing both sides of the equation by 5:

$\begin{array}{l}\Rightarrow 5\left|2\mathrm{x}-1\right|-5=20\\ \Rightarrow 5\left|2\mathrm{x}-1\right|=25\\ \Rightarrow \left|2\mathrm{x}-1\right|=5\end{array}$

Understanding that the expression within the absolute value bars can be either positive or negative, we solve for both cases:

Solve for (2x-1) as positive:                 

$\begin{array}{l}\Rightarrow \left|2\mathrm{x}-1\right|=5\\ \Rightarrow 2\mathrm{x}-1=5\\ \Rightarrow 2\mathrm{x}=6\to \mathrm{x}=3\end{array}$                               

Solve for (2x-1) as negative:

$\begin{array}{l}\Rightarrow \left|2\mathrm{x}-1\right|=5\\ \Rightarrow -(2\mathrm{x}-1)=5\\ \Rightarrow -2\mathrm{x}+1=5\\ \Rightarrow -2\mathrm{x}=4\to \mathrm{x}=-2\end{array}$

The sum of the solutions is 3 + (-2) = 1.