Answer :
To determine the range of acceptable weights for your suitcase, we need to write an inequality. The rules state that the weight of the suitcase can vary by at most 7.5 pounds from a base weight. Let's choose 40 pounds as a reference weight.
We'll use [tex]\( x \)[/tex] to represent the weight of the suitcase. The condition that the weight can vary by at most 7.5 pounds from this reference weight gives us the inequality:
[tex]\[ |x - 40| \leq 7.5 \][/tex]
This absolute value inequality means that the difference between the weight of the suitcase and 40 pounds is at most 7.5 pounds.
To solve the absolute value inequality, we'll convert it into a compound inequality:
[tex]\[ -7.5 \leq x - 40 \leq 7.5 \][/tex]
To find the range of acceptable weights, we'll solve for [tex]\( x \)[/tex] by adding 40 to all parts of the inequality:
1. Add 40 to the left part:
[tex]\[ -7.5 + 40 \leq x \][/tex]
[tex]\[ 32.5 \leq x \][/tex]
2. Add 40 to the right part:
[tex]\[ x \leq 7.5 + 40 \][/tex]
[tex]\[ x \leq 47.5 \][/tex]
Combining these results, the inequality for the weight [tex]\( x \)[/tex] becomes:
[tex]\[ 32.5 \leq x \leq 47.5 \][/tex]
Therefore, the weight of your suitcase can be between 32.5 pounds and 47.5 pounds.
We'll use [tex]\( x \)[/tex] to represent the weight of the suitcase. The condition that the weight can vary by at most 7.5 pounds from this reference weight gives us the inequality:
[tex]\[ |x - 40| \leq 7.5 \][/tex]
This absolute value inequality means that the difference between the weight of the suitcase and 40 pounds is at most 7.5 pounds.
To solve the absolute value inequality, we'll convert it into a compound inequality:
[tex]\[ -7.5 \leq x - 40 \leq 7.5 \][/tex]
To find the range of acceptable weights, we'll solve for [tex]\( x \)[/tex] by adding 40 to all parts of the inequality:
1. Add 40 to the left part:
[tex]\[ -7.5 + 40 \leq x \][/tex]
[tex]\[ 32.5 \leq x \][/tex]
2. Add 40 to the right part:
[tex]\[ x \leq 7.5 + 40 \][/tex]
[tex]\[ x \leq 47.5 \][/tex]
Combining these results, the inequality for the weight [tex]\( x \)[/tex] becomes:
[tex]\[ 32.5 \leq x \leq 47.5 \][/tex]
Therefore, the weight of your suitcase can be between 32.5 pounds and 47.5 pounds.