Q33. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{5x}{9}-11=-51$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-72$.

Step 1. Write the given equation.

The given equation is “$\frac{5x}{9}-11=-51$”.

Step 2. Solve the given equation.

Solving,

 

$\frac{5x}{9}-11=-51$  (Given equation)

 

$\frac{5x}{9}-11+11=-51+11$  (Add 11 to both sides)

 

$\frac{5x}{9}=-40$  (Simplify)

 

$\frac{5x}{9}\times \frac{9}{5}=-40\times \frac{9}{5}$  (Multiply both sides by $\frac{9}{5}$)

 

$x=-72$  (Simplify)

 

So, $x=-72$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=-72$ in the given equation $\frac{5x}{9}-11=-51$ to get,

 

$\begin{array}{l}\frac{5\left(-72\right)}{9}-11=-51\\ 5\left(-8\right)-11=-51\\ -40-11=-51\\ -51=-51\end{array}$

 

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.