# How do you solve and check your solutions to -1.2=z/4.6-2.7?

Feb 10, 2017

See the entire solution and verification process below:

#### Explanation:

First, add $\textcolor{red}{2.7}$ to each side of the equation to isolate the $z$ term while keeping the equation balanced:

$- 1.2 + \textcolor{red}{2.7} = \frac{z}{4.6} - 2.7 + \textcolor{red}{2.7}$

$1.5 = \frac{z}{4.6} - 0$

$1.5 = \frac{z}{4.6}$

Now, multiply each side of the equation by $\textcolor{red}{4.6}$ to solve for $z$ while keeping the equation balanced:

$\textcolor{red}{4.6} \times 1.5 = \textcolor{red}{4.6} \times \frac{z}{4.6}$

$6.9 = \cancel{\textcolor{red}{4.6}} \times \frac{z}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4.6}}}}$

$6.9 = z$

$z = 6.9$

To check the solution we need to substitute $6.9$ for $z$ in the original problem and calculate the right side of the equation to ensure it equals $- 1.2$

$- 1.2 = \frac{6.9}{4.6} - 2.7$

$- 1.2 = 1.5 - 2.7$

$- 1.2 = - 1.2$

Because both sides of the equation equal $- 1.2$ we have verified the solution we obtained is correct.