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Which graph represents the solution to 2x + 4 < 2? A + -1 0 1 + -5 -4 -3 -2 2 3 4 5 B + + -5 -4 -3 -2 -1 0 1 2 3 4 5 + -5 -4 -3 -2 -1 0 1 2 3 4 5 + -5 -4 -3 -2 -1 0 1 2 3 4 5 + 4 +7

Which graph represents the solution to 2x + 4 < 2? A + -1 0 1 + -5 -4 -3 -2 2 3 4 5 B + + -5 -4 -3 -2 -1 0 1 2 3 4 5 + -5 -4 -3 -2 -1 0 1 2 3 4 5 + -5 -4 -3 -2 -1 0 1 2 3 4 5 + 4 +7

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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**Title: Solving Linear Inequalities and Graph Representation** **Question:** Which graph represents the solution to the inequality \(2x + 4 < 2\)? **Explanation:** To solve the inequality \(2x + 4 < 2\), follow these steps: 1. Subtract 4 from both sides: \[ 2x < -2 \] 2. Divide both sides by 2: \[ x < -1 \] **Graph Analysis:** Examine each graph (A, B, C, D) to determine which one correctly represents \(x < -1\). - **Graph A:** Displays a number line with shading to the left of \(-1\) and an open circle at \(-1\), indicating that \(x\) is less than \(-1\) but does not include \(-1\). - **Graph B:** Displays a number line with shading to the left of \(-1\) and an open circle at \(-1\). - **Graph C:** Displays a number line with shading to the right of \(-1\) and a filled circle at \(-1\), indicating \(x \geq -1\), which is incorrect for this inequality. - **Graph D:** Displays a number line with shading to the left, starting from \(-1\) with a filled circle, indicating \(x \leq -1\), which is also incorrect for this inequality. **Correct Answer:** - **Graph A** represents the solution \(x < -1\) accurately with correct shading and an open circle, matching the inequality solution.
Transcribed Image Text:**Title: Solving Linear Inequalities and Graph Representation** **Question:** Which graph represents the solution to the inequality \(2x + 4 < 2\)? **Explanation:** To solve the inequality \(2x + 4 < 2\), follow these steps: 1. Subtract 4 from both sides: \[ 2x < -2 \] 2. Divide both sides by 2: \[ x < -1 \] **Graph Analysis:** Examine each graph (A, B, C, D) to determine which one correctly represents \(x < -1\). - **Graph A:** Displays a number line with shading to the left of \(-1\) and an open circle at \(-1\), indicating that \(x\) is less than \(-1\) but does not include \(-1\). - **Graph B:** Displays a number line with shading to the left of \(-1\) and an open circle at \(-1\). - **Graph C:** Displays a number line with shading to the right of \(-1\) and a filled circle at \(-1\), indicating \(x \geq -1\), which is incorrect for this inequality. - **Graph D:** Displays a number line with shading to the left, starting from \(-1\) with a filled circle, indicating \(x \leq -1\), which is also incorrect for this inequality. **Correct Answer:** - **Graph A** represents the solution \(x < -1\) accurately with correct shading and an open circle, matching the inequality solution.
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