Question

question
solve for x. express your answer as a proper or improper fraction in simplest terms.
$-dfrac{1}{2} = dfrac{4}{9}x + dfrac{5}{6}$
answer
attempt 1 out of 2

Explanation:

Step1: Subtract $\frac{5}{6}$ from both sides

$-\frac{1}{2} - \frac{5}{6} = \frac{4}{9}x + \frac{5}{6} - \frac{5}{6}$
First, find a common denominator for the left - hand side. The common denominator of 2 and 6 is 6. So, $-\frac{1}{2}=-\frac{3}{6}$. Then $-\frac{3}{6}-\frac{5}{6}=-\frac{3 + 5}{6}=-\frac{8}{6}=-\frac{4}{3}$. The right - hand side simplifies to $\frac{4}{9}x$. So we have $-\frac{4}{3}=\frac{4}{9}x$.

Step2: Solve for $x$ by multiplying both sides by $\frac{9}{4}$

$x=-\frac{4}{3}\times\frac{9}{4}$
The 4 in the numerator and denominator cancels out. Then, $\frac{- 9}{3}=-3$.

Answer:

$-3$