Question

In Exercises \(32-37\), solve each equation for the unknown quantity. Check your answers. $$-\frac{4}{9}=-\frac{5}{6}-x$$

Short answer

Answer: The value of x in the given equation is -7/18.

Step-by-step solution

Note down the given equation

The given equation is: $$-\frac{4}{9}=-\frac{5}{6}-x$$

Add \(5/6\) to both sides of the equation

To isolate x, we need to eliminate the constant term on the right side. To do this, we will add \(\frac{5}{6}\) to both sides of the equation: $$-\frac{4}{9} + \frac{5}{6} = -\frac{5}{6} + \frac{5}{6} - x$$

Simplify both sides of the equation

Now, we will simplify both sides of the equation by finding the common denominator of the fractions and adding them together: $$\frac{-8+15}{18} = -x$$ $$\frac{7}{18} = -x$$

Multiply both sides of the equation by -1

To get x alone on one side, we need to eliminate the negative sign. We do this by multiplying both sides of the equation by -1: $$-\frac{7}{18} = x$$

Check the solution

Now, we plug the value of x back into the original equation to make sure it satisfies the equation: $$-\frac{4}{9}=-\frac{5}{6}-\left(-\frac{7}{18}\right)$$ $$-\frac{4}{9}=-\frac{5}{6}+\frac{7}{18}$$ $$-\frac{4}{9}=\frac{-15+7}{18}$$ $$-\frac{4}{9}=\frac{-8}{18}$$ $$-\frac{4}{9}=-\frac{4}{9}$$ The solution is correct. #Answer# $$x=-\frac{7}{18}$$