Q19. - Algebra 1

Question

Solve each equation. Check your solution. (Lesson 2-4)

$\frac{z+6}{3}=\frac{2z}{4}$

Step-by-Step Solution

Answer

$z=12$ is the solution of the given equation.

Step 1. Given equation.

$\frac{z+6}{3}=\frac{2z}{4}$

Step 2. Description of step.

The given equation can be solved as,

$$\begin{gathered} \frac{z+6}{3}=\frac{2z}{4} \\ \frac{z+6}{3}=\frac{z}{2} \\ \left(z+6\right)\times 2=z\times 3 \\ \Rightarrow 2z+12=3z \\ \Rightarrow 3z-2z=12 \\ \Rightarrow z=12 \end{gathered}$$

Step 3. Check solution.

In order to check the solution, put the value of z back in the given equation and see if it satisfies the equation, i.e. of left hand side is equals to right hand side, as:

$$\begin{gathered} \frac{z+6}{3}=\frac{2z}{4} \\ \Rightarrow \frac{\left(12\right)+6}{3}=\frac{2\left(12\right)}{4} \\ \Rightarrow \frac{18}{3}=\frac{24}{4} \\ \Rightarrow 6=6 \\ \Rightarrow \text{true} \end{gathered}$$

Hence, the solution $z=12$ satisfies the equation.