Which of the following values are solutions to the inequality -2 < -7+5x? {:[" I. "7," II. "1," III. "3]:} 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. Start with the inequality -2 1. I. Test x = 7. 1 < 7 is true, so 7 is a solution.Test x=7: Test the second value. II. Test x = 1. 1 < 1 is false, so 1 is not a solution.Test x=1: Test the third value. III. Test x = 3. 1 < 3 is true, so 3 is a solution.Test x=3: Combine the results from steps 2, 3, and 4 to determine which of the given values are solutions to the inequality. From the tests, we have determined that: I. 7 is a solution. II. 1 is not a solution. III. 3 is a solution. Therefore, the values that are solutions to the inequality are I and III.

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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

-2<-7+5 x ?

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\begin{array}{lll}\text { I. } 7 & \text { II. } 1 & \text { III. } 3\end{array}

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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. $\newline$ Start with the inequality -2 < -7 + 5x. $\newline$ Add $7$ to both sides to isolate the term with $x$ on one side. $\newline$ -2 + 7 < -7 + 7 + 5x $\newline$ 5 < 5x $\newline$ Now, divide both sides by $5$ to solve for $x$ . $\newline$ \frac{5}{5} < \frac{5x}{5} $\newline$ 1 < x $\newline$ This means that $x$ must be greater than $7$ $0$ .
Test values: Test the given values to see if they satisfy the inequality x > 1. $\newline$ I. Test $x = 7$ . $\newline$ 1 < 7 is true, so $7$ is a solution.
Test $x=7$ : Test the second value. $\newline$ II. Test $x = 1$ . $\newline$ 1 < 1 is false, so $1$ is not a solution.
Test $x=1$ : Test the third value. $\newline$ III. Test $x = 3$ . $\newline$ 1 < 3 is true, so $3$ is a solution.
Test $x=3$ : Combine the results from steps $2$ , $3$ , and $4$ to determine which of the given values are solutions to the inequality. $\newline$ From the tests, we have determined that: $\newline$ I. $7$ is a solution. $\newline$ II. $1$ is not a solution. $\newline$ III. $3$ is a solution. $\newline$ Therefore, the values that are solutions to the inequality are I and III.