Which of the following values are solutions to the inequality -9 >= -7+4x? I. 6 II. -8 III. 5 None I only II only III only I and II I and III II and III I, II and III

Understand Inequality: Analyze the inequality to understand what we are looking for. We need to find the values of x that satisfy the inequality -9 ≥ -7 + 4x.Isolate Variable x: Isolate the variable x on one side of the inequality. To do this, we can add 7 to both sides of the inequality to get: -9 + 7 ≥ 4x -2 ≥ 4xDivide by 4: Divide both sides of the inequality by 4 to solve for x. -2 / 4 ≥ x -0.5 ≥ x This means that x must be less than or equal to -0.5 to satisfy the inequality.Test Solutions: Test each of the given values to see if they satisfy the inequality x ≤ -0.5. I. 6: 6 is not less than or equal to -0.5, so it is not a solution. II. -8: -8 is less than or equal to -0.5, so it is a solution. III. 5: 5 is not less than or equal to -0.5, so it is not a solution.Determine Correct Choice: Determine the correct choice based on the solutions found. Only value II (-8) is a solution to the inequality. So the answer 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

-9 \geq-7+4 x ?

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6

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II.

-8

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III.

5

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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: Analyze the inequality to understand what we are looking for. $\newline$ We need to find the values of $x$ that satisfy the inequality $-9 \geq -7 + 4x$ .
Isolate Variable $x$ : Isolate the variable $x$ on one side of the inequality. $\newline$ To do this, we can add $7$ to both sides of the inequality to get: $\newline$ $-9 + 7 \geq 4x$ $\newline$ $-2 \geq 4x$
Divide by $4$ : Divide both sides of the inequality by $4$ to solve for $x$ . $-\frac{2}{4} \geq x$ $-0.5 \geq x$ This means that $x$ must be less than or equal to $-0.5$ to satisfy the inequality.
Test Solutions: Test each of the given values to see if they satisfy the inequality $x \leq -0.5$ . $\newline$ I. $6$ : $6$ is not less than or equal to $-0.5$ , so it is not a solution. $\newline$ II. $-8$ : $-8$ is less than or equal to $-0.5$ , so it is a solution. $\newline$ III. $5$ : $5$ is not less than or equal to $-0.5$ , so it is not a solution.
Determine Correct Choice: Determine the correct choice based on the solutions found. $\newline$ Only value $II (-8)$ is a solution to the inequality. $\newline$ So the answer is ＂ $II$ only.＂