Which of the following is a solution to the inequality below? -42 >= (-80)/(k)+5 (1) k=8 (2) k=4 (3) k=1 (4) k=10

Understand Inequality: Understand the inequality and what is being asked. We need to find the value of k that makes the inequality -42 >= (-80)/k + 5 true.Test k = 8: Test the first option, k = 8. Substitute k = 8 into the inequality and simplify. -42 >= (-80)/8 + 5 -42 >= -10 + 5 -42 >= -5 This is not true because -42 is not greater than or equal to -5.Test k = 4: Test the second option, k = 4. Substitute k = 4 into the inequality and simplify. -42 >= (-80)/4 + 5 -42 >= -20 + 5 -42 >= -15 This is true because -42 is less than -15, which satisfies the inequality.Final Solution: Since we have found a value of k that satisfies the inequality, we do not need to test the remaining options.

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Which of the following is a solution to the inequality below? $\newline$ $-42 \geq \frac{-80}{k}+5$ $\newline$ $($ $1)$ $k=8$ $\newline$ $($ $2)$ $k=4$ $\newline$ $($ $3)$ $k=1$ $\newline$ $($ $4)$ $k=10$

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Math Problems

Grade 8

Solutions to inequalities

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Q. Which of the following is a solution to the inequality below?

\newline

-42 \geq \frac{-80}{k}+5

\newline

(

1)

k=8

\newline

(

2)

k=4

\newline

(

3)

k=1

\newline

(

4)

k=10

Understand Inequality: Understand the inequality and what is being asked. $\newline$ We need to find the value of $k$ that makes the inequality $-42 \geq (-80)/k + 5$ true.
Test $k = 8$ : Test the first option, $k = 8$ . Substitute $k = 8$ into the inequality and simplify. $-42 \geq (-80)/8 + 5$ $-42 \geq -10 + 5$ $-42 \geq -5$ This is not true because $-42$ is not greater than or equal to $-5$ .
Test $k = 4$ : Test the second option, $k = 4$ . $\newline$ Substitute $k = 4$ into the inequality and simplify. $\newline$ $-42 \geq (-80)/4 + 5$ $\newline$ $-42 \geq -20 + 5$ $\newline$ $-42 \geq -15$ $\newline$ This is true because $-42$ is less than $-15$ , which satisfies the inequality.
Final Solution: Since we have found a value of $k$ that satisfies the inequality, we do not need to test the remaining options.