Question

solve for m.
$4 - \frac{3}{5}m = \frac{6}{5}m + 2$
$m = \square$

Explanation:

Step1: Add $\frac{3}{5}m$ to both sides

To eliminate the $-\frac{3}{5}m$ on the left, we add $\frac{3}{5}m$ to each side. So the equation becomes:
$4 = \frac{6}{5}m + \frac{3}{5}m + 2$

Step2: Combine like terms for m

Combine $\frac{6}{5}m$ and $\frac{3}{5}m$. Since they have the same denominator, we add the numerators:
$\frac{6}{5}m + \frac{3}{5}m = \frac{9}{5}m$. Now the equation is $4 = \frac{9}{5}m + 2$

Step3: Subtract 2 from both sides

Subtract 2 from each side to isolate the term with $m$:
$4 - 2 = \frac{9}{5}m$
$2 = \frac{9}{5}m$

Step4: Multiply both sides by $\frac{5}{9}$

To solve for $m$, multiply both sides by the reciprocal of $\frac{9}{5}$, which is $\frac{5}{9}$:
$m = 2 \times \frac{5}{9}$
$m = \frac{10}{9}$

Answer:

$\frac{10}{9}$