Question

1. write an equation that represents the following statement: the product of five and a number, x, decreased by seventeen is the same as 52.
2. what is the solution to: \\(\frac{-14x - 8}{6} + 8.5 = -4.5\\)

Explanation:

Question 15

Step1: Identify the product

The product of five and \( x \) is \( 5x \).

Step2: Decrease by seventeen

Decreasing \( 5x \) by seventeen gives \( 5x - 17 \).

Step3: Set equal to 52

The phrase "is the same as" means equality, so we set \( 5x - 17 \) equal to 52.

Step1: Subtract 8.5 from both sides

Subtract 8.5 from each side to isolate the fraction: \(\frac{-14x - 8}{6} + 8.5 - 8.5 = -4.5 - 8.5\)
Simplify: \(\frac{-14x - 8}{6} = -13\)

Step2: Multiply both sides by 6

Multiply each side by 6 to eliminate the denominator: \(6 \times \frac{-14x - 8}{6} = -13 \times 6\)
Simplify: \(-14x - 8 = -78\)

Step3: Add 8 to both sides

Add 8 to each side: \(-14x - 8 + 8 = -78 + 8\)
Simplify: \(-14x = -70\)

Step4: Divide by -14

Divide each side by -14: \(\frac{-14x}{-14} = \frac{-70}{-14}\)
Simplify: \(x = 5\)

Answer:

\( 5x - 17 = 52 \)

Question 16