Question

#7 \\(\frac{3}{2}(x + 1) = 3\\) #8 \\(-12 = \frac{4}{3}(2x - 1)\\)

Explanation:

Step1: Eliminate fraction for #7

Multiply both sides by 2:
$$2 \times \frac{3}{2}(x+1) = 3 \times 2$$
$$3(x+1) = 6$$

Step2: Isolate parenthetical term for #7

Divide both sides by 3:
$$\frac{3(x+1)}{3} = \frac{6}{3}$$
$$x+1 = 2$$

Step3: Solve for x for #7

Subtract 1 from both sides:
$$x+1-1 = 2-1$$
$$x = 1$$

Step4: Eliminate fraction for #8

Multiply both sides by 3:
$$-12 \times 3 = \frac{4}{3}(2x-1) \times 3$$
$$-36 = 4(2x-1)$$

Step5: Isolate parenthetical term for #8

Divide both sides by 4:
$$\frac{-36}{4} = \frac{4(2x-1)}{4}$$
$$-9 = 2x-1$$

Step6: Solve for x for #8

Add 1, then divide by 2:
$$-9+1 = 2x-1+1$$
$$-8 = 2x$$
$$\frac{-8}{2} = \frac{2x}{2}$$
$$x = -4$$

Answer:

For #7: $x=1$
For #8: $x=-4$