Question

1. solve: \\(\frac{3}{2} (10 - 4d) = - 27\\)

Explanation:

Step1: Multiply both sides by 2/3

To eliminate the fraction, multiply both sides of the equation $\frac{3}{2}(10 - 4d) = -27$ by $\frac{2}{3}$.
$$\frac{2}{3} \times \frac{3}{2}(10 - 4d) = \frac{2}{3} \times (-27)$$
Simplifying both sides, we get:
$$10 - 4d = -18$$

Step2: Subtract 10 from both sides

Subtract 10 from each side to isolate the term with $d$.
$$10 - 4d - 10 = -18 - 10$$
Simplifying gives:
$$-4d = -28$$

Step3: Divide by -4

Divide both sides by -4 to solve for $d$.
$$\frac{-4d}{-4} = \frac{-28}{-4}$$
Simplifying, we find:
$$d = 7$$

Answer:

$d = 7$