Question

how do i indicate absolute value of a section in math to you
Answer
my ls are my vertical bars for this problem 4 l2x-1l-2=10
Answer
give me a simmiliar question
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
Answer
what are the answers
Answer
give me a simmilir question wih the 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!
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!
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!
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!
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!
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!