# How do you solve and write the following in interval notation: 2x < 10 and -5x < 5?

Jun 11, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the first inequality as:

$2 x < 10$

$\frac{2 x}{\textcolor{red}{2}} < \frac{10}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} < 5$

$x < 5$

Step 2) Solve the second equality. Remember, when multiplying or dividing an inequality by a negative number you must reverse the inequality operator:

$- 5 x < 5$

$\frac{- 5 x}{\textcolor{red}{- 5}} \textcolor{red}{>} \frac{5}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} x}{\cancel{\textcolor{red}{- 5}}} \textcolor{red}{>} - 1$

$x > - 1$

Step 3) Combine the solutions and write the solution in interval notation:

$x > - 1$ and $x < 5$

$\left(- 1 , 5\right)$