# How do you solve and graph 4x-3<2x?

Aug 13, 2015

$x < \frac{3}{2}$

#### Explanation:

You can solve this inequality by isolating $x$ on one side.

This can be done in three steps. First, add $3$ to both sides of the inequality to get

$4 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} < 2 x + 3$

$4 x < 2 x + 3$

Now add $- 2 x$ to both sides of the inequality

$4 x - 2 x < \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} + 3$

$2 x < 3$

Finally, divide both sides of the inequality by $2$ to isolate $x$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} < \frac{3}{2}$

$x < \textcolor{g r e e n}{\frac{3}{2}}$

To graph the solution set for this inequality, draw a dotted vertical line parallel to the $y$-axis that goes through $x = \frac{3}{2}$.

Since you want all the $x$ values that are smaller than $\frac{3}{2}$, shade the region to the left of $x = \frac{3}{2}$.

The dotted line signifies that $x = \frac{3}{2}$ is not a part of the solution set.

graph{x<3/2 [-10, 10, -5, 5]}