Question

Solve each equation. Check your solution.

$14=\frac{6+z}{-2}$

Short answer

The solution of the given equation is $z=-34$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$14=\frac{6+z}{-2}$”.

Step 2. Solve the given equation.

Solving,

$14=\frac{6+z}{-2}$ (Given equation)

$14\times \left(-2\right)=\frac{6+z}{-2}\times \left(-2\right)$ (Multiply both sides by $-2$)

$-28=6+z$ (Simplify)

$-28-6=6+z-6$ (Subtract 6 from both sides)

$-34=z$ (Simplify)

$z=-34$ (Write the variable on the left-hand side)

So, $z=-34$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $z=-34$in the given equation $14=\frac{6+z}{-2}$to get,

$\begin{array}{l}14=\frac{6-34}{-2}\\ 14=\frac{-28}{-2}\\ 14=14\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.