How do you solve 16.7<3(x+4 1/2)?

Jul 13, 2017

See a solution process below:

Explanation:

First, we need to convert the mixed number to a fraction:

$16.7 < 3 \left(x + 4 \frac{1}{2}\right)$

$16.7 < 3 \left(x + \left[4 + \frac{1}{2}\right]\right)$

$16.7 < 3 \left(x + \left[\left(4 \times \frac{2}{2}\right) + \frac{1}{2}\right]\right)$

$16.7 < 3 \left(x + \left[\frac{8}{2} + \frac{1}{2}\right]\right)$

$16.7 < 3 \left(x + \frac{9}{2}\right)$

$16.7 < 3 \left(x + 4.5\right)$

Next, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$16.7 < \textcolor{red}{3} \left(x + 4.5\right)$

$16.7 < \left(\textcolor{red}{3} \times x\right) + \left(\textcolor{red}{3} \times 4.5\right)$

$16.7 < 3 x + 13.5$

Then, subtract $\textcolor{red}{13.5}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$16.7 - \textcolor{red}{13.5} < 3 x + 13.5 - \textcolor{red}{13.5}$

$3.2 < 3 x + 0$

$3.2 < 3 x$

Now, divide each side of the inequality by $\textcolor{red}{3}$ to solve for $x$ while keeping the inequality balanced:

$\frac{3.2}{\textcolor{red}{3}} < \frac{3 x}{\textcolor{red}{3}}$

$1.0 \overline{6} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}}$

$1.0 \overline{6} < x$

We can state the solution in terms of $x$ by reversing or "flipping" the entire inequality:

$x > 1.0 \overline{6}$