Which of the following values are solutions to the inequality -5+2x <= 6? I. 14 II. 4 III. -2 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 -5 + 2x <= 6. Add 5 to both sides to isolate the term with x. -5 + 2x + 5 <= 6 + 5 2x <= 11 Now, divide both sides by 2 to solve for x. 2x / 2 <= 11 / 2 x <= 5.5Add 5 to Both Sides: Check each value to see if it satisfies the inequality x <= 5.5. I. For x = 14, check if 14 <= 5.5. This is not true, so 14 is not a solution.Divide by 2: Check the second value. II. For x = 4, check if 4 <= 5.5. This is true, so 4 is a solution.Check x Values: Check the third value. III. For x = -2, check if -2 <= 5.5. This is true, so -2 is a solution.Combine Results: Combine the results from steps 2, 3, and 4 to determine which of the given values are solutions to the inequality. 14 is not a solution. 4 is a solution. -2 is a solution. Therefore, the values that are solutions to the inequality are 4 and -2.

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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

-5+2 x \leq 6 ?

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14

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II.

4

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III.

-2

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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 $-5 + 2x \leq 6$ . $\newline$ Add $5$ to both sides to isolate the term with $x$ . $\newline$ $-5 + 2x + 5 \leq 6 + 5$ $\newline$ $2x \leq 11$ $\newline$ Now, divide both sides by $2$ to solve for $x$ . $\newline$ $\frac{2x}{2} \leq \frac{11}{2}$ $\newline$ $x \leq 5.5$
Add $5$ to Both Sides: Check each value to see if it satisfies the inequality $x \leq 5.5$ . $\newline$ I. For $x = 14$ , check if $14 \leq 5.5$ . $\newline$ This is not true, so $14$ is not a solution.
Divide by $2$ : Check the second value. $\newline$ II. For $x = 4$ , check if $4 \leq 5.5$ . $\newline$ This is true, so $4$ is a solution.
Check $x$ Values: Check the third value. $\newline$ III. For $x = -2$ , check if $-2 \leq 5.5$ . $\newline$ This is true, so $-2$ is a solution.
Combine Results: Combine the results from steps $2$ , $3$ , and $4$ to determine which of the given values are solutions to the inequality. $\newline$ $14$ is not a solution. $\newline$ $4$ is a solution. $\newline$ $-2$ is a solution. $\newline$ Therefore, the values that are solutions to the inequality are $4$ and $-2$ .