Question Find the value of $y$ given $y \leq -75$ . Options: A) $y=75$ , B) $y=-74$ , C) $y>-75$ , D) $y=-75$ .

Studdy Solution

STEP 1

Assumptions
1. The inequality given is $y \leq -75$ .
2. We need to determine which of the given options could be true given the inequality.

STEP 2

Analyze each option against the inequality $y \leq -75$ .

STEP 3

Option A suggests that $y = 75$ . We need to check if $75$ satisfies the inequality $y \leq -75$ .

STEP 4

Compare $75$ with $-75$ .
$75 \leq -75$

STEP 5

Determine if the comparison is true or false.
This comparison is false because $75$ is greater than $-75$ . Therefore, option A cannot be true.

STEP 6

Option B suggests that $y = -74$ . We need to check if $-74$ satisfies the inequality $y \leq -75$ .

STEP 7

Compare $-74$ with $-75$ .
$-74 \leq -75$

STEP 8

Determine if the comparison is true or false.
This comparison is false because $-74$ is greater than $-75$ . Therefore, option B cannot be true.

STEP 9

Option C suggests that $y > -75$ . We need to check if a number greater than $-75$ satisfies the inequality $y \leq -75$ .

STEP 10

Understand the meaning of the inequality $y > -75$ .
This means that $y$ is any number greater than $-75$ , which does not satisfy the original inequality $y \leq -75$ . Therefore, option C cannot be true.

STEP 11

Option D suggests that $y = -75$ . We need to check if $-75$ satisfies the inequality $y \leq -75$ .

STEP 12

Compare $-75$ with $-75$ .
$-75 \leq -75$

STEP 13

Determine if the comparison is true or false.
This comparison is true because $-75$ is equal to $-75$ . Therefore, option D could be true.
The correct answer is D $y=-75$ .

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