Question

1. \\(\frac{1}{9}(2m - 16) = \frac{1}{3}(2m + 4)\\)

Explanation:

Step1: Eliminate denominators

Multiply both sides by 9:
$$9\times\frac{1}{9}(2m - 16) = 9\times\frac{1}{3}(2m + 4)$$
Simplify to get:
$$2m - 16 = 3(2m + 4)$$

Step2: Expand right-hand side

Distribute the 3:
$$2m - 16 = 6m + 12$$

Step3: Isolate variable terms

Subtract $2m$ from both sides:
$$-16 = 4m + 12$$

Step4: Isolate constant terms

Subtract 12 from both sides:
$$-16 - 12 = 4m$$
$$-28 = 4m$$

Step5: Solve for m

Divide both sides by 4:
$$m = \frac{-28}{4}$$

Answer:

$m = -7$