**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.

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)

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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Question

**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

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

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Your answer is inco

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

Solution

by Bartleby Expert

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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.

Solution

by Bartleby Expert

SEE SOLUTION

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