Question

Solve each equation. Check your solution.

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

Short answer

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

Step-by-step solution

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.