Which of the following values are solutions to the inequality 4x+10 > -6? I. -1 II. -4 III. 4 None I only II only III only I and II I and III II and III I, II and III

Solve for x: Solve the inequality for x. We start by subtracting 10 from both sides of the inequality to isolate the term with x. 4x + 10 - 10 > -6 - 10 4x > -16 Now, divide both sides by 4 to solve for x. 4x / 4 > -16 / 4 x > -4Test x values: Test each value to see if it satisfies the inequality x > -4. I. For x = -1: -1 > -4 This is true, so -1 is a solution.Test x=-1: Test the second value. II. For x = -4: -4 > -4 This is false, as -4 is not greater than -4, so -4 is not a solution.Test x=-4: Test the third value. III. For x = 4: 4 > -4 This is true, so 4 is a solution.Test x=4: Combine the results from steps 2, 3, and 4 to determine which of the given choices are correct. From our tests, we found that: I. -1 is a solution. II. -4 is not a solution. III. 4 is a solution. 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

4 x+10>-6 ?

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-1

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II.

-4

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III.

4

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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 for x: Solve the inequality for x. $\newline$ We start by subtracting $10$ from both sides of the inequality to isolate the term with $x$ . $\newline$ 4x + 10 - 10 > -6 - 10 $\newline$ 4x > -16 $\newline$ Now, divide both sides by $4$ to solve for $x$ . $\newline$ \frac{4x}{4} > \frac{-16}{4} $\newline$ x > -4
Test $x$ values: Test each value to see if it satisfies the inequality x > -4. $\newline$ I. For $x = -1$ : $\newline$ -1 > -4 $\newline$ This is true, so $-1$ is a solution.
Test $x=-1$ : Test the second value. $\newline$ II. For $x = -4$ : $\newline$ -4 > -4 $\newline$ This is false, as $-4$ is not greater than $-4$ , so $-4$ is not a solution.
Test $x=-4$ : Test the third value. $\newline$ III. For $x = 4$ : $\newline$ 4 > -4 $\newline$ This is true, so $4$ is a solution.
Test $x=4$ : Combine the results from steps $2$ , $3$ , and $4$ to determine which of the given choices are correct. $\newline$ From our tests, we found that: $\newline$ I. $-1$ is a solution. $\newline$ II. $-4$ is not a solution. $\newline$ III. $4$ is a solution. $\newline$ Therefore, the correct answer is I and III.