Which of the following values are solutions to the inequality 9 >= -1-x ? I. -2 II. -10 III. -11 None I only II only III only I and II I and III II and III I, II and III

Understand Inequality Solution: Understand the inequality and what it means to be a solution. To be a solution to the inequality 9 >= -1-x, a number must satisfy the condition when substituted for x.Test Value -2: Test the first value, I. -2. Substitute x with -2 in the inequality 9 >= -1-x. 9 >= -1-(-2) 9 >= -1+2 9 >= 1 This is true, so -2 is a solution to the inequality.Test Value -10: Test the second value, II. -10. Substitute x with -10 in the inequality 9 >= -1-x. 9 >= -1-(-10) 9 >= -1+10 9 >= 9 This is also true, so -10 is a solution to the inequality.Test Value -11: Test the third value, III. -11. Substitute x with -11 in the inequality 9 >= -1-x. 9 >= -1-(-11) 9 >= -1+11 9 >= 10 This is false, so -11 is not a solution to the inequality.Combine Results: Combine the results from Steps 2, 3, and 4 to determine which of the given choices are correct. We found that -2 and -10 are solutions, but -11 is not. Therefore, the correct choice is ＂I and II＂.

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Math Problems

Grade 8

Solutions to inequalities

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Q. Which of the following values are solutions to the inequality

9 \geq-1-x

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-2

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II.

-10

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III.

-11

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None

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I only

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II only

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III only

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I and II

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I and III

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II and III

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I, II and III

Understand Inequality Solution: Understand the inequality and what it means to be a solution. $\newline$ To be a solution to the inequality $9 \geq -1-x$ , a number must satisfy the condition when substituted for $x$ .
Test Value $-2$ : Test the first value, $I. -2$ . Substitute $x$ with $-2$ in the inequality $9 \geq -1-x$ . $9 \geq -1-(-2)$ $9 \geq -1+2$ $9 \geq 1$ This is true, so $-2$ is a solution to the inequality.
Test Value $-10$ : Test the second value, II. $-10$ . Substitute $x$ with $-10$ in the inequality $9 \geq -1-x$ . $9 \geq -1-(-10)$ $9 \geq -1+10$ $9 \geq 9$ This is also true, so $-10$ is a solution to the inequality.
Test Value $-11$ : Test the third value, III. $-11$ . Substitute $x$ with $-11$ in the inequality $9 \geq -1-x$ . $9 \geq -1-(-11)$ $9 \geq -1+11$ $9 \geq 10$ This is false, so $-11$ is not a solution to the inequality.
Combine Results: Combine the results from Steps $2$ , $3$ , and $4$ to determine which of the given choices are correct. $\newline$ We found that $-2$ and $-10$ are solutions, but $-11$ is not. $\newline$ Therefore, the correct choice is ＂I and II＂.