# How do you graph and solve 3/2 abs( 2x-5 ) -2= 7?

Mar 11, 2016

$x = - \frac{1}{2}$ or $x = \frac{11}{2}$

#### Explanation:

First thing to do would be to simplify things a little.

$\frac{3}{2} \left\mid 2 x - 5 \right\mid - 2 = 7 \iff \frac{3}{2} \left\mid 2 x - 5 \right\mid = 9 \iff \left\mid 2 x - 5 \right\mid = 6$

Next we draw a graph of ${y}_{1} = \left\mid 2 x - 5 \right\mid$ and ${y}_{2} = 6$ to see where they intersect. The point of intersection corresponds to a solution.

To graph ${y}_{1} = \left\mid 2 x - 5 \right\mid$, we know that minimum occurs when ${y}_{1} = 0$ at $x = \frac{5}{2}$. Therefore, the graph is symmetrical about the line $x = 2.5$. The graph is a V-shape.
graph{abs(2x-5) [-7, 12, -3, 7]}
The graph ${y}_{2} = 6$ is just a horizontal line at the height $y = 6$.
graph{6+0x [-16.5, 21.5, -8, 12]}
When graphed together, they look like

They intersect at $\left(- 0.5 , 6\right)$ and $\left(5.5 , 6\right)$.