How do you solve and graph 7x-12<8?

Dec 8, 2017

See a solution process below:

Explanation:

First, add $\textcolor{red}{12}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$7 x - 12 + \textcolor{red}{12} < 8 + \textcolor{red}{12}$

$7 x - 0 < 20$

$7 x < 20$

Now, divide each side of the inequality by $\textcolor{red}{7}$ to solve for $x$ while keeping the inequality balanced:

$\frac{7 x}{\textcolor{red}{7}} < \frac{20}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}} < \frac{20}{7}$

$x < \frac{20}{7}$

Or

$x < 2.857$ rounded to the nearest thousandth.

To graph this we will draw a vertical line at $\frac{20}{7}$ on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the left side of the line because the inequality operator contains a "less than" clause:

graph{x < 20/7 [-10, 10, -5, 5]}