Which of the following values are solutions to the inequality 6+4x <= -9 ? I. 1 II. -2 III. -1 None I only II only III only I and II I and III II and III I, II and III

Solve Inequality for x: Solve the inequality for x. Start with the inequality 6 + 4x <= -9. Subtract 6 from both sides to isolate the term with x. 4x <= -9 - 6 4x <= -15 Now, divide both sides by 4 to solve for x. x <= -15 / 4 x <= -3.75Test x Values: Test each of the given values to see if they satisfy the inequality x <= -3.75. I. Test if x = 1 is a solution. 1 <= -3.75 This is false, so 1 is not a solution.Test x=1: Test the second value. II. Test if x = -2 is a solution. -2 <= -3.75 This is false, so -2 is not a solution.Test x=-2: Test the third value. III. Test if x = -1 is a solution. -1 <= -3.75 This is false, so -1 is not a solution.Test x=-1: Determine which of the given choices is correct based on the tests. None of the values I (1), II (-2), or III (-1) are solutions to the inequality because all of them are greater than -3.75. The correct choice is ＂None.＂

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Math Problems

Grade 8

Solutions to inequalities

Full solution

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

6+4 x \leq-9

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1

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II.

-2

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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

Solve Inequality for x: Solve the inequality for x. $\newline$ Start with the inequality $6 + 4x \leq -9$ . $\newline$ Subtract $6$ from both sides to isolate the term with $x$ . $\newline$ $4x \leq -9 - 6$ $\newline$ $4x \leq -15$ $\newline$ Now, divide both sides by $4$ to solve for $x$ . $\newline$ $x \leq -\frac{15}{4}$ $\newline$ $x \leq -3.75$
Test $x$ Values: Test each of the given values to see if they satisfy the inequality $x \leq -3.75$ . $\newline$ I. Test if $x = 1$ is a solution. $\newline$ $1 \leq -3.75$ $\newline$ This is false, so $1$ is not a solution.
Test $x=1$ : Test the second value. $\newline$ II. Test if $x = -2$ is a solution. $\newline$ $-2 \leq -3.75$ $\newline$ This is false, so $-2$ is not a solution.
Test $x=-2$ : Test the third value. $\newline$ III. Test if $x = -1$ is a solution. $\newline$ $-1 \leq -3.75$ $\newline$ This is false, so $-1$ is not a solution.
Test $x=-1$ : Determine which of the given choices is correct based on the tests. $\newline$ None of the values I ( $1$ ), II ( $-2$ ), or III ( $-1$ ) are solutions to the inequality because all of them are greater than $-3.75$ . $\newline$ The correct choice is ＂None.＂