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Solve the compound inequality. 3u-1<8 and 4u+4 < 28 Write the solution in interval notation. If there is no solution, enter Ø. (0,0) [0,0) (0,0) [0,0) ? 8. olo

Solve the compound inequality. 3u-1<8 and 4u+4 < 28 Write the solution in interval notation. If there is no solution, enter Ø. (0,0) [0,0) (0,0) [0,0) ? 8. olo

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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**Solve the Compound Inequality** \[ 3u - 1 < 8 \] \[ \text{and} \] \[ 4u + 4 \leq 28 \] *Write the solution in interval notation. If there is no solution, enter \(\varnothing\).* --- ### Explanation This exercise involves solving a compound inequality, which is a combination of two inequalities connected by the word "and." The solution must satisfy both inequalities simultaneously. #### Steps to Solve: 1. **First Inequality: \(3u - 1 < 8\)** - Add 1 to both sides: \(3u < 9\). - Divide both sides by 3: \(u < 3\). 2. **Second Inequality: \(4u + 4 \leq 28\)** - Subtract 4 from both sides: \(4u \leq 24\). - Divide both sides by 4: \(u \leq 6\). 3. **Combine Solutions:** - The solution must satisfy both \(u < 3\) and \(u \leq 6\). - Therefore, the combined solution is \(u < 3\). #### Interval Notation: - The solution in interval notation is \((-∞, 3)\). **Note:** The solution involves using the correct interval notation symbols. The answer box allows for a set of symbols to input your answer, including infinity symbols \((∞, -∞)\), interval brackets \(([, [, ], ]\)), and the option to denote no solution with \(\varnothing\). Use the correct format to present your answer in terms of interval notation accurately.
Transcribed Image Text:**Solve the Compound Inequality** \[ 3u - 1 < 8 \] \[ \text{and} \] \[ 4u + 4 \leq 28 \] *Write the solution in interval notation. If there is no solution, enter \(\varnothing\).* --- ### Explanation This exercise involves solving a compound inequality, which is a combination of two inequalities connected by the word "and." The solution must satisfy both inequalities simultaneously. #### Steps to Solve: 1. **First Inequality: \(3u - 1 < 8\)** - Add 1 to both sides: \(3u < 9\). - Divide both sides by 3: \(u < 3\). 2. **Second Inequality: \(4u + 4 \leq 28\)** - Subtract 4 from both sides: \(4u \leq 24\). - Divide both sides by 4: \(u \leq 6\). 3. **Combine Solutions:** - The solution must satisfy both \(u < 3\) and \(u \leq 6\). - Therefore, the combined solution is \(u < 3\). #### Interval Notation: - The solution in interval notation is \((-∞, 3)\). **Note:** The solution involves using the correct interval notation symbols. The answer box allows for a set of symbols to input your answer, including infinity symbols \((∞, -∞)\), interval brackets \(([, [, ], ]\)), and the option to denote no solution with \(\varnothing\). Use the correct format to present your answer in terms of interval notation accurately.
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