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What is the solution to the inequality 3x + 4 > -2? A -4 -3 -2 -1 0 1 2 4 B + + -4 -3 -2 -1 1 4

What is the solution to the inequality 3x + 4 > -2? A -4 -3 -2 -1 0 1 2 4 B + + -4 -3 -2 -1 1 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:** What is the solution to the inequality \(3x + 4 > -2\)? **Graphs Explanation:** The image presents four different number lines labeled A, B, C, and D, each representing a potential solution to the inequality. - **Option A:** Shows a number line with an open circle at \(-2\), extending to the left to \(-4\). The shading goes from the circle leftwards, indicating all numbers less than \(-2\). - **Option B:** Shows a number line with an open circle at \(x = -2\), extending to the right to \(x = 4\). The shading goes from the circle rightwards, indicating all numbers greater than \(-2\). - **Option C:** Shows a number line with an open circle at \(x = -3\), extending to the right to \(x = 4\). The shading indicates all numbers greater than \(-3\). - **Option D:** Shows a number line with an open circle at \(x = -1\), extending to the right to \(x = 4\). The shading indicates all numbers greater than \(-1\). **Solution:** To solve the inequality \(3x + 4 > -2\): 1. Subtract 4 from both sides: \(3x > -6\). 2. Divide both sides by 3: \(x > -2\). Therefore, the correct graph is **Option B**, which depicts all numbers greater than \(-2\).
Transcribed Image Text:**Problem Statement:** What is the solution to the inequality \(3x + 4 > -2\)? **Graphs Explanation:** The image presents four different number lines labeled A, B, C, and D, each representing a potential solution to the inequality. - **Option A:** Shows a number line with an open circle at \(-2\), extending to the left to \(-4\). The shading goes from the circle leftwards, indicating all numbers less than \(-2\). - **Option B:** Shows a number line with an open circle at \(x = -2\), extending to the right to \(x = 4\). The shading goes from the circle rightwards, indicating all numbers greater than \(-2\). - **Option C:** Shows a number line with an open circle at \(x = -3\), extending to the right to \(x = 4\). The shading indicates all numbers greater than \(-3\). - **Option D:** Shows a number line with an open circle at \(x = -1\), extending to the right to \(x = 4\). The shading indicates all numbers greater than \(-1\). **Solution:** To solve the inequality \(3x + 4 > -2\): 1. Subtract 4 from both sides: \(3x > -6\). 2. Divide both sides by 3: \(x > -2\). Therefore, the correct graph is **Option B**, which depicts all numbers greater than \(-2\).
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