# How do you solve and check your solutions to 3.2+x/2.5=4.6?

Feb 13, 2017

See the entire solution and verification process below:

#### Explanation:

First, subtract $\textcolor{red}{3.2}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3.2 + \frac{x}{2.5} - \textcolor{red}{3.2} = 4.6 - \textcolor{red}{3.2}$

$3.2 - \textcolor{red}{3.2} + \frac{x}{2.5} = 1.4$

$0 + \frac{x}{2.5} = 1.4$

$\frac{x}{2.5} = 1.4$

Now, multiply each side of the equation by $\textcolor{red}{2.5}$ to solve for $x$ while keeping the equation balanced:

$\textcolor{red}{2.5} \times \frac{x}{2.5} = \textcolor{red}{2.5} \times 1.4$

$\cancel{\textcolor{red}{2.5}} \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2.5}}}} = \textcolor{red}{2.5} \times 1.4$

$x = 3.5$

To verify the solution we substitute $3.5$ for $x$ in the left side of the equation and calculate to ensure the left side of the equation is equal to the right side of the equation:

$3.2 + \frac{x}{2.5} = 4.6$ becomes:

$3.2 + \frac{3.5}{2.5} = 4.6$

$3.2 + 1.4 = 4.6$

$4.6 = 4.6$

Because both sides of the equation are equal $x = 1.4$ is a valid solution.