Question

(17) $-\frac{1}{12}(24 - 12a) = 13$
(18) $2(6.2b + 1) = -47.6$

Explanation:

Solving Equation (17): \(-\frac{1}{12}(24 - 12\alpha) = 13\)

Step 1: Distribute the \(-\frac{1}{12}\)

Multiply each term inside the parentheses by \(-\frac{1}{12}\):

$$ -\frac{1}{12} \times 24 + (-\frac{1}{12}) \times (-12\alpha) = 13 $$

Simplify each term:

$$ -2 + \alpha = 13 $$

Step 2: Solve for \(\alpha\)

Add 2 to both sides of the equation:

$$ \alpha = 13 + 2 $$

$$ \alpha = 15 $$

Solving Equation (18): \(2(6.2b + 1) = -47.6\)

Step 1: Divide both sides by 2

$$ \frac{2(6.2b + 1)}{2} = \frac{-47.6}{2} $$

Simplify:

$$ 6.2b + 1 = -23.8 $$

Step 2: Subtract 1 from both sides

$$ 6.2b = -23.8 - 1 $$

$$ 6.2b = -24.8 $$

Step 3: Divide both sides by 6.2

$$ b = \frac{-24.8}{6.2} $$

$$ b = -4 $$

Final Answers

For equation (17): \(\alpha = \boldsymbol{15}\)
For equation (18): \(b = \boldsymbol{-4}\)

Answer:

Solving Equation (17): \(-\frac{1}{12}(24 - 12\alpha) = 13\)

Step 1: Distribute the \(-\frac{1}{12}\)

Multiply each term inside the parentheses by \(-\frac{1}{12}\):

$$ -\frac{1}{12} \times 24 + (-\frac{1}{12}) \times (-12\alpha) = 13 $$

Simplify each term:

$$ -2 + \alpha = 13 $$

Step 2: Solve for \(\alpha\)

Add 2 to both sides of the equation:

$$ \alpha = 13 + 2 $$

$$ \alpha = 15 $$

Solving Equation (18): \(2(6.2b + 1) = -47.6\)

Step 1: Divide both sides by 2

$$ \frac{2(6.2b + 1)}{2} = \frac{-47.6}{2} $$

Simplify:

$$ 6.2b + 1 = -23.8 $$

Step 2: Subtract 1 from both sides

$$ 6.2b = -23.8 - 1 $$

$$ 6.2b = -24.8 $$

Step 3: Divide both sides by 6.2

$$ b = \frac{-24.8}{6.2} $$

$$ b = -4 $$

Final Answers

For equation (17): \(\alpha = \boldsymbol{15}\)
For equation (18): \(b = \boldsymbol{-4}\)