Which of the following values are solutions to the inequality 8 > -5+x ? I. 10 II. 5 III. 13 None I only II only III only I and II I and III II and III I, II and III

Understand the inequality: Understand the inequality. We are given the inequality 8 > -5 + x, and we need to find which of the given values (I. 10, II. 5, III. 13) satisfy this inequality.Solve for x: Solve the inequality for x. Add 5 to both sides of the inequality to isolate x. 8 > -5 + x 8 + 5 > x 13 > x This means that any value of x that is less than 13 is a solution to the inequality.Check values: Check each value to see if it satisfies the inequality. I. For x = 10: 13 > 10 is true, so 10 is a solution.Check second value: Check the second value. II. For x = 5: 13 > 5 is true, so 5 is a solution.Check third value: Check the third value. III. For x = 13: 13 > 13 is false, because 13 is not less than 13, so 13 is not a solution.Combine results: Combine the results from steps 3, 4, and 5 to find the final answer. Values I (10) and II (5) are solutions to the inequality, but III (13) is not. 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

8>-5+x

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10

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II.

5

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III.

13

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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 the inequality: Understand the inequality. $\newline$ We are given the inequality 8 > -5 + x, and we need to find which of the given values (I. $10$ , II. $5$ , III. $13$ ) satisfy this inequality.
Solve for x: Solve the inequality for $x$ . Add $5$ to both sides of the inequality to isolate $x$ . 8 > -5 + x 8 + 5 > x 13 > x This means that any value of $x$ that is less than $13$ is a solution to the inequality.
Check values: Check each value to see if it satisfies the inequality. $\newline$ I. For $x = 10$ : $\newline$ 13 > 10 is true, so $10$ is a solution.
Check second value: Check the second value. $\newline$ II. For $x = 5$ : $\newline$ 13 > 5 is true, so $5$ is a solution.
Check third value: Check the third value. $\newline$ III. For $x = 13$ : $\newline$ 13 > 13 is false, because $13$ is not less than $13$ , so $13$ is not a solution.
Combine results: Combine the results from steps $3$ , $4$ , and $5$ to find the final answer. $\newline$ Values I ( $10$ ) and II ( $5$ ) are solutions to the inequality, but III ( $13$ ) is not. $\newline$ The correct choice is ＂I and II＂.