# Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 211: 25

f=−2 or f=1.5

#### Work Step by Step

|4f+1|−2=5⟶ add 2 to each side |4f+1|−2+2=5+2⟶ add |4f+1|=7⟶ definition of absolute value 4f+1=−7 or 4f+1=7⟶ solve each equation 4f+1=−7⟶ subtract 1 from each side 4f+1−1=−7−1⟶ subtract 4f=−8⟶ divide each side by 4 4f÷4=−8÷4⟶ divide f=−2 OR 4f+1=7⟶ subtract 1 from each side 4f+1−1=7−1⟶ subtract 4f=6⟶ divide each side by 4 4f÷4=6÷4⟶ divide f=1.5

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
The text passage contains a mathematical problem involving absolute value equations, and it provides a step-by-step solution to the problem, including the final answers.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 211: 25

f=−2 or f=1.5

#### Work Step by Step

|4f+1|−2=5⟶ add 2 to each side |4f+1|−2+2=5+2⟶ add |4f+1|=7⟶ definition of absolute value 4f+1=−7 or 4f+1=7⟶ solve each equation 4f+1=−7⟶ subtract 1 from each side 4f+1−1=−7−1⟶ subtract 4f=−8⟶ divide each side by 4 4f÷4=−8÷4⟶ divide f=−2 OR 4f+1=7⟶ subtract 1 from each side 4f+1−1=7−1⟶ subtract 4f=6⟶ divide each side by 4 4f÷4=6÷4⟶ divide f=1.5

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
user
The text passage contains a mathematical problem involving absolute value equations, and it provides a step-by-step solution to the problem, including the final answers.

TYPE: SINGLE_QUESTION_WITH_ANSWER