Question
how do i indicate absolute value of a section in math to you
Answers
Answered by
GPT-4o mini
To indicate the absolute value of a number or expression in math, you can use vertical bars. For example, the absolute value of \( x \) is represented as \( |x| \).
If you're referring to the absolute value of a section of an equation or expression, you can include it in a similar way. For example:
- The absolute value of \( x - 3 \) is written as \( |x - 3| \).
- If you want to express the absolute value of a sum, you might write \( |a + b| \).
Feel free to provide specific examples if you need help with a particular expression!
If you're referring to the absolute value of a section of an equation or expression, you can include it in a similar way. For example:
- The absolute value of \( x - 3 \) is written as \( |x - 3| \).
- If you want to express the absolute value of a sum, you might write \( |a + b| \).
Feel free to provide specific examples if you need help with a particular expression!
Answer
my ls are my vertical bars for this problem 4 l2x-1l-2=10
Answered by
GPT-4o mini
It looks like you're using \( l \) to represent vertical bars as in absolute value. Based on what you've written, the equation you provided can be expressed as:
\[
4 |2x - 1| - 2 = 10
\]
To solve this equation, follow these steps:
1. First, isolate the absolute value expression. Add 2 to both sides:
\[
4 |2x - 1| = 12
\]
2. Next, divide both sides by 4:
\[
|2x - 1| = 3
\]
3. Now, set up the two cases for the absolute value:
- Case 1: \( 2x - 1 = 3 \)
- Case 2: \( 2x - 1 = -3 \)
4. Solve each case independently:
**Case 1:**
\[
2x - 1 = 3
\]
\[
2x = 4
\]
\[
x = 2
\]
**Case 2:**
\[
2x - 1 = -3
\]
\[
2x = -2
\]
\[
x = -1
\]
5. The solutions to the original equation are \( x = 2 \) and \( x = -1 \).
If you have any further questions or need additional assistance, feel free to ask!
\[
4 |2x - 1| - 2 = 10
\]
To solve this equation, follow these steps:
1. First, isolate the absolute value expression. Add 2 to both sides:
\[
4 |2x - 1| = 12
\]
2. Next, divide both sides by 4:
\[
|2x - 1| = 3
\]
3. Now, set up the two cases for the absolute value:
- Case 1: \( 2x - 1 = 3 \)
- Case 2: \( 2x - 1 = -3 \)
4. Solve each case independently:
**Case 1:**
\[
2x - 1 = 3
\]
\[
2x = 4
\]
\[
x = 2
\]
**Case 2:**
\[
2x - 1 = -3
\]
\[
2x = -2
\]
\[
x = -1
\]
5. The solutions to the original equation are \( x = 2 \) and \( x = -1 \).
If you have any further questions or need additional assistance, feel free to ask!
Answer
give me a simmiliar question
Answered by
GPT-4o mini
Sure! Here’s a similar problem involving absolute value:
**Problem:**
Solve the equation:
\[
3 |x + 4| + 6 = 15
\]
Feel free to solve it, and let me know if you'd like any assistance!
**Problem:**
Solve the equation:
\[
3 |x + 4| + 6 = 15
\]
Feel free to solve it, and let me know if you'd like any assistance!
Answer
3lx+4l+6=15
Subtract 6 both sides
3 lx+4l=9
Divide by 3 on both sides so lx+4l=3
So subtract 4 to both sides
x=-1 or lx-4l add 4 to both sides x=7
is that right also another similiar problem please
Subtract 6 both sides
3 lx+4l=9
Divide by 3 on both sides so lx+4l=3
So subtract 4 to both sides
x=-1 or lx-4l add 4 to both sides x=7
is that right also another similiar problem please
Answered by
GPT-4o mini
Great effort on solving the problem! Let's correct and clarify a few steps in your solution, and then I'll provide another similar problem.
### Original equation:
\[
3 |x + 4| + 6 = 15
\]
### Step 1: Subtract 6 from both sides
\[
3 |x + 4| = 9
\]
### Step 2: Divide by 3
\[
|x + 4| = 3
\]
### Step 3: Set up two cases for the absolute value:
**Case 1:**
\[
x + 4 = 3
\]
Subtract 4 from both sides:
\[
x = -1
\]
**Case 2:**
\[
x + 4 = -3
\]
Subtract 4 from both sides:
\[
x = -7
\]
So the correct solutions are:
\[
x = -1 \quad \text{and} \quad x = -7
\]
---
### Another Similar Problem:
Solve the equation:
\[
2 |3x - 5| - 4 = 10
\]
Feel free to try solving it, and let me know if you need any help!
### Original equation:
\[
3 |x + 4| + 6 = 15
\]
### Step 1: Subtract 6 from both sides
\[
3 |x + 4| = 9
\]
### Step 2: Divide by 3
\[
|x + 4| = 3
\]
### Step 3: Set up two cases for the absolute value:
**Case 1:**
\[
x + 4 = 3
\]
Subtract 4 from both sides:
\[
x = -1
\]
**Case 2:**
\[
x + 4 = -3
\]
Subtract 4 from both sides:
\[
x = -7
\]
So the correct solutions are:
\[
x = -1 \quad \text{and} \quad x = -7
\]
---
### Another Similar Problem:
Solve the equation:
\[
2 |3x - 5| - 4 = 10
\]
Feel free to try solving it, and let me know if you need any help!
Answer
what are the answers
Answered by
GPT-4o mini
Let's solve the equation step by step:
Given the equation:
\[
2 |3x - 5| - 4 = 10
\]
### Step 1: Add 4 to both sides
\[
2 |3x - 5| = 14
\]
### Step 2: Divide by 2
\[
|3x - 5| = 7
\]
### Step 3: Set up two cases for the absolute value
**Case 1:**
\[
3x - 5 = 7
\]
Add 5 to both sides:
\[
3x = 12
\]
Divide by 3:
\[
x = 4
\]
**Case 2:**
\[
3x - 5 = -7
\]
Add 5 to both sides:
\[
3x = -2
\]
Divide by 3:
\[
x = -\frac{2}{3}
\]
### Final Answers
The solutions to the equation \( 2 |3x - 5| - 4 = 10 \) are:
\[
x = 4 \quad \text{and} \quad x = -\frac{2}{3}
\]
If you have any further questions or need clarification, feel free to ask!
Given the equation:
\[
2 |3x - 5| - 4 = 10
\]
### Step 1: Add 4 to both sides
\[
2 |3x - 5| = 14
\]
### Step 2: Divide by 2
\[
|3x - 5| = 7
\]
### Step 3: Set up two cases for the absolute value
**Case 1:**
\[
3x - 5 = 7
\]
Add 5 to both sides:
\[
3x = 12
\]
Divide by 3:
\[
x = 4
\]
**Case 2:**
\[
3x - 5 = -7
\]
Add 5 to both sides:
\[
3x = -2
\]
Divide by 3:
\[
x = -\frac{2}{3}
\]
### Final Answers
The solutions to the equation \( 2 |3x - 5| - 4 = 10 \) are:
\[
x = 4 \quad \text{and} \quad x = -\frac{2}{3}
\]
If you have any further questions or need clarification, feel free to ask!
Answer
give me a simmilir question wih the answers
Answered by
GPT-4o mini
Here’s a similar problem along with the solution:
**Problem:**
Solve the equation:
\[
5 |2x + 1| - 3 = 17
\]
### Step-by-step Solution:
1. **Add 3 to both sides:**
\[
5 |2x + 1| = 20
\]
2. **Divide by 5:**
\[
|2x + 1| = 4
\]
3. **Set up two cases for the absolute value:**
**Case 1:**
\[
2x + 1 = 4
\]
Subtract 1 from both sides:
\[
2x = 3
\]
Divide by 2:
\[
x = \frac{3}{2}
\]
**Case 2:**
\[
2x + 1 = -4
\]
Subtract 1 from both sides:
\[
2x = -5
\]
Divide by 2:
\[
x = -\frac{5}{2}
\]
### Final Answers
The solutions to the equation \( 5 |2x + 1| - 3 = 17 \) are:
\[
x = \frac{3}{2} \quad \text{and} \quad x = -\frac{5}{2}
\]
Feel free to ask if you need more problems or further clarification!
**Problem:**
Solve the equation:
\[
5 |2x + 1| - 3 = 17
\]
### Step-by-step Solution:
1. **Add 3 to both sides:**
\[
5 |2x + 1| = 20
\]
2. **Divide by 5:**
\[
|2x + 1| = 4
\]
3. **Set up two cases for the absolute value:**
**Case 1:**
\[
2x + 1 = 4
\]
Subtract 1 from both sides:
\[
2x = 3
\]
Divide by 2:
\[
x = \frac{3}{2}
\]
**Case 2:**
\[
2x + 1 = -4
\]
Subtract 1 from both sides:
\[
2x = -5
\]
Divide by 2:
\[
x = -\frac{5}{2}
\]
### Final Answers
The solutions to the equation \( 5 |2x + 1| - 3 = 17 \) are:
\[
x = \frac{3}{2} \quad \text{and} \quad x = -\frac{5}{2}
\]
Feel free to ask if you need more problems or further clarification!