How do you solve 1.2x + 8 < 9.6 and graph the solution graph the solution on a number line?

Feb 19, 2018

$x < 1.333$

Explanation:

Move the $8$ over so you have

$1.2 x < 1.6$

Then divide both sides by $1.2$. This will give you

$x < \frac{1.6}{1.2}$

$x < 1.333 \ldots$

So in the end, you have $x < 1.333$ (notice that the sign doesn't change because there is no multiplication/division by a negative).

Then you would just put an arrow going left to negative infinity starting at $1.333$ with an open circle. :)

Feb 19, 2018

See a solution process below:

Explanation:

First, subtract $\textcolor{red}{8}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$1.2 x + 8 - \textcolor{red}{8} < 9.6 - \textcolor{red}{8}$

$1.2 x + 0 < 1.6$

$1.2 x < 1.6$

Next, divide each side of the inequality by $\textcolor{red}{1.2}$ to solve for $x$ while keeping the inequality balanced:

$\frac{1.2 x}{\textcolor{red}{1.2}} < \frac{1.6}{\textcolor{red}{1.2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{1.2}}} x}{\cancel{\textcolor{red}{1.2}}} < \frac{10}{10} \times \frac{1.6}{\textcolor{red}{1.2}}$

$x < \frac{16}{12}$

$x < \frac{4}{3}$

Or

$x < 1 \frac{1}{3}$

To graph this on the number line we need to put a hollow point at $1 \frac{1}{3}$ on the number line because the inequality does not contain an "or equal to" clause. Therefore, $1 \frac{1}{3}$ is not part of the solution set.

Then from that point we draw an arrow to the left because the inequality is a "less than" operator: 