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3. Solve each absolute value inequality. Express each answer using set-builder notation and using interval notation. Graph each inequality's solution set on a number line graph. A) | 6x +15-7<11 Solution Set-builder notation, Interval notation, Number-line graph B) 2x +11-132-8 Solution Set-builder notation Interval notation Number-line graph

3. Solve each absolute value inequality. Express each answer using set-builder notation and using interval notation. Graph each inequality's solution set on a number line graph. A) | 6x +15-7<11 Solution Set-builder notation, Interval notation, Number-line graph B) 2x +11-132-8 Solution Set-builder notation Interval notation Number-line graph

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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**Solving Absolute Value Inequalities** **3. Solve each absolute value inequality. Express each answer using set-builder notation and interval notation. Graph each inequality’s solution set on a number line graph.** **A)** \[ |6x + 15| - 7 < 11 \] - **Solution:** - **Set-builder notation:** - **Interval notation:** - **Number-line graph:** **B)** \[ |2x + 11| - 13 \geq -8 \] - **Solution:** - **Set-builder notation:** - **Interval notation:** - **Number-line graph:** **Explanation for Graph Use:** For each problem, after solving the inequality you will graph the solution on a number line to visually represent the range of values that satisfy the inequality. This involves: 1. Plotting the critical points where the inequality changes. 2. Using open or closed circles based on whether the inequality is strict ("<" or ">") or inclusive ("≤" or "≥"). 3. Shading the region that represents all solutions to the inequality. This exercise helps in understanding how absolute value inequalities define a range of possible values.
Transcribed Image Text:**Solving Absolute Value Inequalities** **3. Solve each absolute value inequality. Express each answer using set-builder notation and interval notation. Graph each inequality’s solution set on a number line graph.** **A)** \[ |6x + 15| - 7 < 11 \] - **Solution:** - **Set-builder notation:** - **Interval notation:** - **Number-line graph:** **B)** \[ |2x + 11| - 13 \geq -8 \] - **Solution:** - **Set-builder notation:** - **Interval notation:** - **Number-line graph:** **Explanation for Graph Use:** For each problem, after solving the inequality you will graph the solution on a number line to visually represent the range of values that satisfy the inequality. This involves: 1. Plotting the critical points where the inequality changes. 2. Using open or closed circles based on whether the inequality is strict ("<" or ">") or inclusive ("≤" or "≥"). 3. Shading the region that represents all solutions to the inequality. This exercise helps in understanding how absolute value inequalities define a range of possible values.
**Section 2.8** **2. Solve each absolute value equation.** A) \(\left| \frac{1}{5}x - 4 \right| + 1 = 11\) Solution ____________________________ B) \(\left| 3x^2 - 17x + 10 \right| = 10\) Solution ____________________________
Transcribed Image Text:**Section 2.8** **2. Solve each absolute value equation.** A) \(\left| \frac{1}{5}x - 4 \right| + 1 = 11\) Solution ____________________________ B) \(\left| 3x^2 - 17x + 10 \right| = 10\) Solution ____________________________
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