Which of the following values are solutions to the inequality 1 > x+1 ? I. -3 II. 0 III. -1 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 1 > x + 1 and we need to find which of the given values satisfy this inequality.Simplify the inequality: Simplify the inequality. Subtract 1 from both sides of the inequality to isolate x. 1 - 1 > x + 1 - 1 0 > x This simplifies to x < 0, which means we are looking for values of x that are less than 0.Test -3: Test the first value, I. -3. Check if -3 satisfies the inequality x < 0. -3 < 0 This is true, so -3 is a solution to the inequality.Test 0: Test the second value, II. 0. Check if 0 satisfies the inequality x < 0. 0 < 0 This is not true, so 0 is not a solution to the inequality.Test -1: Test the third value, III. -1. Check if -1 satisfies the inequality x < 0. -1 < 0 This is true, so -1 is a solution to the inequality.Combine results: Combine the results from steps 3, 4, and 5. We found that -3 and -1 are solutions to the inequality, but 0 is not. Therefore, the correct answer is ＂I and III＂.

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Math Problems

Grade 8

Solutions to inequalities

Full solution

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

1>x+1

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-3

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II.

0

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III.

-1

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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 1 > x + 1 and we need to find which of the given values satisfy this inequality.
Simplify the inequality: Simplify the inequality. $\newline$ Subtract $1$ from both sides of the inequality to isolate $x$ . $\newline$ 1 - 1 > x + 1 - 1 $\newline$ 0 > x $\newline$ This simplifies to x < 0, which means we are looking for values of $x$ that are less than $0$ .
Test $-3$ : Test the first value, $I. -3$ . $\newline$ Check if $-3$ satisfies the inequality x < 0. $\newline$ -3 < 0 $\newline$ This is true, so $-3$ is a solution to the inequality.
Test $0$ : Test the second value, II. $0$ . Check if $0$ satisfies the inequality x < 0. 0 < 0 This is not true, so $0$ is not a solution to the inequality.
Test $-1$ : Test the third value, III. $-1$ . $\newline$ Check if $-1$ satisfies the inequality x < 0. $\newline$ -1 < 0 $\newline$ This is true, so $-1$ is a solution to the inequality.
Combine results: Combine the results from steps $3$ , $4$ , and $5$ . We found that $-3$ and $-1$ are solutions to the inequality, but $0$ is not. Therefore, the correct answer is ＂I and III＂.