# How do you solve 2.5(x-3)+1.7x=10.8(x+1.5)?

Jan 15, 2017

See entire solution process below:

#### Explanation:

First step is to expand the terms in parenthesis:

$\textcolor{red}{2.5} \left(x - 3\right) + 1.7 x = \textcolor{b l u e}{10.8} \left(x + 1.5\right)$

$\left(\textcolor{red}{2.5} \times x\right) - \left(\textcolor{red}{2.5} \times 3\right) + 1.7 x = \left(\textcolor{b l u e}{10.8} \times x\right) + \left(\textcolor{b l u e}{10.8} \times 1.5\right)$

$2.5 x - 7.5 + 1.7 x = 10.8 x + 16.2$

Now group and combine like terms:

$2.5 x + 1.7 x - 7.5 = 10.8 x + 16.2$

$4.2 x - 7.5 = 10.8 x + 16.2$

Next, we subtract the necessary terms to isolate the $x$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$4.2 x - 7.5 - \textcolor{red}{4.2 x} - \textcolor{b l u e}{16.2} = 10.8 x + 16.2 - \textcolor{red}{4.2 x} - \textcolor{b l u e}{16.2}$

$4.2 x - \textcolor{red}{4.2 x} - 7.5 - \textcolor{b l u e}{16.2} = 10.8 x - \textcolor{red}{4.2 x} + 16.2 - \textcolor{b l u e}{16.2}$

$0 - 7.5 - \textcolor{b l u e}{16.2} = 10.8 x - \textcolor{red}{4.2 x} + 0$

$- 23.7 = 6.6 x$

Now, we can divide each side of the equation by $\textcolor{red}{6.6}$ to solve for $x$ while keeping the equation balanced:

$- \frac{23.7}{\textcolor{red}{6.6}} = \frac{6.6 x}{\textcolor{red}{6.6}}$

$- 3.59 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6.6}}} x}{\cancel{\textcolor{red}{6.6}}}$

$- 3.59 = x$

$x = - 3.59$ rounded to the nearest hundredth