Martin Ward
07/06/2024 · Junior High School
Solve each equation. \( \begin{array}{lll}\text { 25. }|x+4|=8 & \text { 26. }|x-5|=12 & \text { 27. }|2+x|=10 \\ \text { 28. }|8-x|=1 & \text { 29. }|x-2|=9 & \text { 30. }|x+5|=11\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve each of the absolute value equations, we will consider the definition of absolute value, which states that \( |a| = b \) implies \( a = b \) or \( a = -b \).
### 25. \( |x+4|=8 \)
This gives us two equations:
1. \( x + 4 = 8 \)
2. \( x + 4 = -8 \)
Solving these:
1. \( x + 4 = 8 \)
\( x = 8 - 4 \)
\( x = 4 \)
2. \( x + 4 = -8 \)
\( x = -8 - 4 \)
\( x = -12 \)
**Solutions:** \( x = 4, -12 \)
---
### 26. \( |x-5|=12 \)
This gives us two equations:
1. \( x - 5 = 12 \)
2. \( x - 5 = -12 \)
Solving these:
1. \( x - 5 = 12 \)
\( x = 12 + 5 \)
\( x = 17 \)
2. \( x - 5 = -12 \)
\( x = -12 + 5 \)
\( x = -7 \)
**Solutions:** \( x = 17, -7 \)
---
### 27. \( |2+x|=10 \)
This gives us two equations:
1. \( 2 + x = 10 \)
2. \( 2 + x = -10 \)
Solving these:
1. \( 2 + x = 10 \)
\( x = 10 - 2 \)
\( x = 8 \)
2. \( 2 + x = -10 \)
\( x = -10 - 2 \)
\( x = -12 \)
**Solutions:** \( x = 8, -12 \)
---
### 28. \( |8-x|=1 \)
This gives us two equations:
1. \( 8 - x = 1 \)
2. \( 8 - x = -1 \)
Solving these:
1. \( 8 - x = 1 \)
\( -x = 1 - 8 \)
\( -x = -7 \)
\( x = 7 \)
2. \( 8 - x = -1 \)
\( -x = -1 - 8 \)
\( -x = -9 \)
\( x = 9 \)
**Solutions:** \( x = 7, 9 \)
---
### 29. \( |x-2|=9 \)
This gives us two equations:
1. \( x - 2 = 9 \)
2. \( x - 2 = -9 \)
Solving these:
1. \( x - 2 = 9 \)
\( x = 9 + 2 \)
\( x = 11 \)
2. \( x - 2 = -9 \)
\( x = -9 + 2 \)
\( x = -7 \)
**Solutions:** \( x = 11, -7 \)
---
### 30. \( |x+5|=11 \)
This gives us two equations:
1. \( x + 5 = 11 \)
2. \( x + 5 = -11 \)
Solving these:
1. \( x + 5 = 11 \)
\( x = 11 - 5 \)
\( x = 6 \)
2. \( x + 5 = -11 \)
\( x = -11 - 5 \)
\( x = -16 \)
**Solutions:** \( x = 6, -16 \)
---
### Summary of Solutions:
- 25: \( x = 4, -12 \)
- 26: \( x = 17, -7 \)
- 27: \( x = 8, -12 \)
- 28: \( x = 7, 9 \)
- 29: \( x = 11, -7 \)
- 30: \( x = 6, -16 \)
Quick Answer
- 25: \( x = 4, -12 \)
- 26: \( x = 17, -7 \)
- 27: \( x = 8, -12 \)
- 28: \( x = 7, 9 \)
- 29: \( x = 11, -7 \)
- 30: \( x = 6, -16 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit