# How do you solve and graph 5-5x>4(3-x)?

Jul 2, 2017

See a solution process below:

#### Explanation:

First, expand the terms on the right side of the inequality by multiplying the terms inside the parenthesis by the term outside the parenthesis:

$5 - 5 x > \textcolor{red}{4} \left(3 - x\right)$

$5 - 5 x > \left(\textcolor{red}{4} \times 3\right) - \left(\textcolor{red}{4} \times x\right)$

$5 - 5 x > 12 - 4 x$

Next, add $\textcolor{red}{5 x}$ and subtract $\textcolor{b l u e}{12}$ from each side of the inequality to solve for $x$ while keeping the inequality balanced:

$- \textcolor{b l u e}{12} + 5 - 5 x + \textcolor{red}{5 x} > - \textcolor{b l u e}{12} + 12 - 4 x + \textcolor{red}{5 x}$

$- 7 - 0 > 0 + \left(- 4 + \textcolor{red}{5}\right) x$

$- 7 > 1 x$

$- 7 > x$

To state the solution in terms of $x$ we can reverse or "flip" the entire inequality:

$x < - 7$