Question

Solve each equation. Check your solution.

$3\left(2z+25\right)-2\left(z-1\right)=78$

Short answer

The required answer is $\frac{1}{4}$.

Step-by-step solution

Step 1- Simplify left side of the equation

Use the distributive property $a\left(b+c\right)=ab+ac$on left side the original equation.

$6z+75-2z+2=78$

Combine the like terms on left side.

$4z+77=78$

Step 2- Isolate the variable z

Perform subtraction of 77 on both the sides of the equation.

$\begin{array}{c}4z+77-77=78-77\\ 4z=1\end{array}$

Perform division of 4 on both sides of the equation.

$\begin{array}{c}\frac{4z}{4}=\frac{1}{4}\\ z=\frac{1}{4}\end{array}$

– Check the obtained value 

Substitute the obtained value of z into the original equation and perform simplification for checking.

$\begin{array}{l}3\left[2\left(\frac{1}{4}\right)+25\right]-2\left[\frac{1}{4}-1\right]\stackrel{?}{=}78\\ 3\left(\frac{51}{2}\right)-2\left(-\frac{3}{4}\right)\stackrel{?}{=}78\\ \frac{153}{2}+\frac{3}{2}\stackrel{?}{=}78\\ 78=78\end{array}$

Step 4- Make the conclusion

As the checking results in equal values on both the sides on substation of obtained value which means that obtained value is correct.