Which of the following values are solutions to the inequality -1-3x <= -1 ? I. -7 II. 0 III. -6 None I only II only III only I and II I and III II and III I, II and III

Simplify and Isolate: Simplify the inequality by adding 1 to both sides to isolate the term with the variable x. -1 - 3x + 1 = 0 / -3 x >= 0Check Solutions: Check each of the given values to see if they satisfy the inequality x >= 0. I. -7: Check if -7 >= 0. -7 is not greater than or equal to 0. So, -7 is not a solution. II. 0: Check if 0 >= 0. 0 is equal to 0. So, 0 is a solution. III. -6: Check if -6 >= 0. -6 is not greater than or equal to 0. So, -6 is not a solution.Identify Correct Choice: Based on the checks, only value II (0) is a solution to the inequality x >= 0. The correct choice is ＂II only.＂

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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

-1-3 x \leq-1

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-7

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II.

0

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III.

-6

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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

Simplify and Isolate: Simplify the inequality by adding $1$ to both sides to isolate the term with the variable $x$ . $-1 - 3x + 1 \leq -1 + 1$ $-3x \leq 0$
Divide and Solve: Divide both sides of the inequality by $-3$ to solve for $x$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-3x / -3 \geq 0 / -3$ $\newline$ $x \geq 0$
Check Solutions: Check each of the given values to see if they satisfy the inequality $x \geq 0$ . $\newline$ I. $-7$ : Check if $-7 \geq 0$ . $\newline$ $-7$ is not greater than or equal to $0$ . $\newline$ So, $-7$ is not a solution. $\newline$ II. $0$ : Check if $0 \geq 0$ . $\newline$ $0$ is equal to $0$ . $\newline$ So, $0$ is a solution. $\newline$ III. $-7$ $1$ : Check if $-7$ $2$ . $\newline$ $-7$ $1$ is not greater than or equal to $0$ . $\newline$ So, $-7$ $1$ is not a solution.
Identify Correct Choice: Based on the checks, only value II $0$ is a solution to the inequality $x \geq 0$ . The correct choice is ＂II only.＂