How do you solve -30+5x <4(6+8x)?

Mar 12, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by $\textcolor{red}{4}$ - the term outside the parenthesis:

$- 30 + 5 x < \textcolor{red}{4} \left(6 + 8 x\right)$

$- 30 + 5 x < \left(\textcolor{red}{4} \times 6\right) + \left(\textcolor{red}{4} \times 8 x\right)$

$- 30 + 5 x < 24 + 32 x$

Next, subtract $\textcolor{red}{5 x}$ and $\textcolor{b l u e}{24}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$- 30 + 5 x - \textcolor{red}{5 x} - \textcolor{b l u e}{24} < 24 + 32 x - \textcolor{red}{5 x} - \textcolor{b l u e}{24}$

$- 30 - \textcolor{b l u e}{24} + 5 x - \textcolor{red}{5 x} < 24 - \textcolor{b l u e}{24} + 32 x - \textcolor{red}{5 x}$

$- 54 + 0 < 0 + \left(32 - 5\right) x$

$- 54 < 27 x$

Now, divide each side of the inequality by $\textcolor{red}{27}$ to solve for $x$ while keeping the inequality balanced:

$- \frac{54}{\textcolor{red}{27}} < \frac{27 x}{\textcolor{red}{27}}$

$- 2 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{27}}} x}{\cancel{\textcolor{red}{27}}}$

$- 2 < x$

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

$x > - 2$