Question

(\frac{1}{5}m + \frac{2}{3} - 2 = m - \frac{2}{5})

Explanation:

Step1: Eliminate fractions

Multiply each term by 15 (LCM of 5, 3) to eliminate denominators:
$15\times\frac{1}{5}m + 15\times\frac{2}{3}-15\times2 = 15m - 15\times\frac{2}{5}$
Simplify: $3m + 10 - 30 = 15m - 6$

Step2: Simplify both sides

Left side: $3m - 20$; Right side: $15m - 6$
Equation: $3m - 20 = 15m - 6$

Step3: Isolate variable terms

Subtract $3m$ from both sides: $-20 = 12m - 6$

Step4: Isolate constant terms

Add 6 to both sides: $-14 = 12m$

Step5: Solve for m

Divide by 12: $m = \frac{-14}{12} = -\frac{7}{6}$

Answer:

$m = -\dfrac{7}{6}$