Question

solve for m.
-4 + \frac{2}{3}m = 3 + \frac{7}{9}m - \frac{8}{9}m
m = \boxed{\space}

Explanation:

Step1: Simplify the right side

Combine like terms: $\frac{7}{9}m - \frac{8}{9}m = -\frac{1}{9}m$. So the equation becomes $-4 + \frac{2}{3}m = 3 - \frac{1}{9}m$.

Step2: Eliminate fractions

Multiply every term by 9 to get rid of denominators: $9\times(-4) + 9\times\frac{2}{3}m = 9\times3 - 9\times\frac{1}{9}m$. This simplifies to $-36 + 6m = 27 - m$.

Step3: Add m to both sides

$-36 + 6m + m = 27 - m + m$ gives $-36 + 7m = 27$.

Step4: Add 36 to both sides

$-36 + 36 + 7m = 27 + 36$ simplifies to $7m = 63$.

Step5: Divide by 7

$\frac{7m}{7} = \frac{63}{7}$ so $m = 9$.

Answer:

$m = 9$