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olve the absolute value equation by writing it as two separate equations. Enter the exact answers in increasing order. P = P = eTextbook and Media Hint First isolate the absolute value on the left-hand side. 13p+71 4 +3=6

olve the absolute value equation by writing it as two separate equations. Enter the exact answers in increasing order. P = P = eTextbook and Media Hint First isolate the absolute value on the left-hand side. 13p+71 4 +3=6

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 Absolute Value Equation** To solve the equation by writing it as two separate equations, follow these steps: Given equation: \[ \frac{|3p + 7|}{4} + 3 = 6 \] **Step 1:** Isolate the absolute value expression. - Subtract 3 from both sides: \[ \frac{|3p + 7|}{4} = 3 \] **Step 2:** Eliminate the fraction by multiplying both sides by 4: - \[ |3p + 7| = 12 \] **Step 3:** Write two separate equations to solve for \( p \): - \( 3p + 7 = 12 \) - \( 3p + 7 = -12 \) **Step 4:** Solve each equation for \( p \). Equation 1: \[ 3p + 7 = 12 \] Subtract 7 from both sides: \[ 3p = 5 \] Divide by 3: \[ p = \frac{5}{3} \] Equation 2: \[ 3p + 7 = -12 \] Subtract 7 from both sides: \[ 3p = -19 \] Divide by 3: \[ p = -\frac{19}{3} \] **Solution:** Enter the exact answers in increasing order: - \( p = -\frac{19}{3} \) - \( p = \frac{5}{3} \) **Additional Resources:** For further reading and practice problems, check out the e-textbook and media resources. **Hint:** First, isolate the absolute value on the left-hand side to simplify the equation-solving process.
Transcribed Image Text:**Solve the Absolute Value Equation** To solve the equation by writing it as two separate equations, follow these steps: Given equation: \[ \frac{|3p + 7|}{4} + 3 = 6 \] **Step 1:** Isolate the absolute value expression. - Subtract 3 from both sides: \[ \frac{|3p + 7|}{4} = 3 \] **Step 2:** Eliminate the fraction by multiplying both sides by 4: - \[ |3p + 7| = 12 \] **Step 3:** Write two separate equations to solve for \( p \): - \( 3p + 7 = 12 \) - \( 3p + 7 = -12 \) **Step 4:** Solve each equation for \( p \). Equation 1: \[ 3p + 7 = 12 \] Subtract 7 from both sides: \[ 3p = 5 \] Divide by 3: \[ p = \frac{5}{3} \] Equation 2: \[ 3p + 7 = -12 \] Subtract 7 from both sides: \[ 3p = -19 \] Divide by 3: \[ p = -\frac{19}{3} \] **Solution:** Enter the exact answers in increasing order: - \( p = -\frac{19}{3} \) - \( p = \frac{5}{3} \) **Additional Resources:** For further reading and practice problems, check out the e-textbook and media resources. **Hint:** First, isolate the absolute value on the left-hand side to simplify the equation-solving process.
Expert Solution
Step 1: Given Expression

Given expression is as follows 

fraction numerator vertical line space 3 p space plus space 7 space vertical line over denominator 4 end fraction space plus space 3 space equals space 6

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Current Attempt in Progress Solve the absolute value equation by writing it as two separate equations. Your answer is partially correct. Enter the exact answers in increasing order. P = P = -19/7 5/3 eTextbook and Media Hint First isolate the absolute value on the left-hand side. Q Search |3p+7 4 +3=6 hp S
Transcribed Image Text:Current Attempt in Progress Solve the absolute value equation by writing it as two separate equations. Your answer is partially correct. Enter the exact answers in increasing order. P = P = -19/7 5/3 eTextbook and Media Hint First isolate the absolute value on the left-hand side. Q Search |3p+7 4 +3=6 hp S
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Follow-up Question

Your answer is inco

**Current Attempt in Progress** **Status:** Your answer is partially correct. **Task:** Solve the absolute value equation by writing it as two separate equations. Equation: \(\frac{|3p + 7|}{4} + 3 = 6\) **Instructions:** Enter the exact answers in increasing order. - \( p = \frac{-19}{7} \) - \( p = \frac{5}{3} \) **eTextbook and Media:** **Hint:** First, isolate the absolute value on the left-hand side.
Transcribed Image Text:**Current Attempt in Progress** **Status:** Your answer is partially correct. **Task:** Solve the absolute value equation by writing it as two separate equations. Equation: \(\frac{|3p + 7|}{4} + 3 = 6\) **Instructions:** Enter the exact answers in increasing order. - \( p = \frac{-19}{7} \) - \( p = \frac{5}{3} \) **eTextbook and Media:** **Hint:** First, isolate the absolute value on the left-hand side.
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