Question

mid year final review
question 16 of 60 (1 point) | question attempt: 1 of 2
felipe has already spent 6 dollars on fabric. he will spend at most 15 dollars on fabric. let’s look at the possible numbers of additional dollars felipe will spend
(a) fill in the blanks to write an inequality that can be used to find x, the number of additional dollars felipe will spend on fabric. choose only from 6 + x, 6 - x, x - 6, 6x, \\(\frac{6}{x}\\), \\(\frac{x}{6}\\), <, ≤, >, ≥, or 15.
inequality:
(b) find the possible numbers of additional dollars felipe will spend on fabric. write your answer as an inequality solved for x.

Explanation:

Step1: Define the total cost

Felipe has spent 6 dollars and will spend \( x \) additional dollars. So the total cost is \( 6 + x \).

Step2: Set up the inequality

He can spend at most 15 dollars, which means the total cost \( 6 + x \) is less than or equal to 15. So the inequality is \( 6 + x \leq 15 \).

Step3: Solve for \( x \)

Subtract 6 from both sides of the inequality: \( 6 + x - 6 \leq 15 - 6 \), which simplifies to \( x \leq 9 \).

Answer:

(a) The inequality is \( 6 + x \leq 15 \) (using \( 6 + x \), \( \leq \), and \( 15 \)).
(b) The solution to the inequality \( 6 + x \leq 15 \) is \( x \leq 9 \).