How do you solve 3.5(x-5.6)+0.03x=4.2x-25.5?

Apr 2, 2017

See the entire solution process below:

Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\left(3.5 \times x\right) - \left(3.5 \times 5.6\right) + 0.03 x = 4.2 x - 25.5$

$3.5 x - 19.6 + 0.03 x = 4.2 x - 25.5$

Next, we can group and combine like terms on the left side of the equation:

$3.5 x + 0.03 x - 19.6 = 4.2 x - 25.5$

$\left(3.5 + 0.03\right) x - 19.6 = 4.2 x - 25.5$

$3.53 x - 19.6 = 4.2 x - 25.5$

Then, subtract $\textcolor{red}{3.53 x}$ and add $\textcolor{b l u e}{25.5}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3.53 x - 19.6 - \textcolor{red}{3.53 x} + \textcolor{b l u e}{25.5} = 4.2 x - 25.5 - \textcolor{red}{3.53 x} + \textcolor{b l u e}{25.5}$

$3.53 x - \textcolor{red}{3.53 x} - 19.6 + \textcolor{b l u e}{25.5} = 4.2 x - \textcolor{red}{3.53 x} - 25.5 + \textcolor{b l u e}{25.5}$

$0 + 5.9 = \left(4.2 - \textcolor{red}{3.53}\right) x - 0$

$5.9 = 0.67 x$

Now, divide each side of the equation by $\textcolor{red}{0.67}$ to solve for $x$ while keeping the equation balanced:

$\frac{5.9}{\textcolor{red}{0.67}} = \frac{0.67 x}{\textcolor{red}{0.67}}$

$8.806 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.67}}} x}{\cancel{\textcolor{red}{0.67}}}$

$8.806 = x$

$x = 8.806$ rounded to the nearest thousandth.