Question
w/8+2=11, and then creating equation from a table
Answers
GPT-4o mini
To solve the equation \( \frac{w}{8} + 2 = 11 \), you can follow these steps:
1. **Isolate the Fraction:**
Subtract 2 from both sides of the equation:
\[
\frac{w}{8} + 2 - 2 = 11 - 2
\]
This simplifies to:
\[
\frac{w}{8} = 9
\]
2. **Eliminate the Fraction:**
To eliminate the fraction, multiply both sides by 8:
\[
8 \times \frac{w}{8} = 9 \times 8
\]
This simplifies to:
\[
w = 72
\]
So, the solution to the equation \( \frac{w}{8} + 2 = 11 \) is \( w = 72 \).
### Creating an Equation from a Table
If you have a table of values, you can create an equation that describes the relationship between the input (often \( x \)) and output (often \( y \)). For example, consider the following table of values:
| \( x \) | \( y \) |
|---------|---------|
| 0 | 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
| 4 | 6 |
#### Steps to Create an Equation:
1. **Identify the Pattern:**
In this table, as \( x \) increases by 1, \( y \) increases by 1 as well.
2. **Write the Equation:**
From the observed pattern, we can infer that the relationship is linear. The \( y \)-intercept (the \( y \) value when \( x = 0 \)) is 2. The slope (the rate of change) is 1 (since \( y \) increases by 1 for each increase of 1 in \( x \)).
Therefore, the equation can be expressed as:
\[
y = x + 2
\]
You would simply follow this approach of observing changes in \( x \) and \( y \) to create an equation based on your specific table of values. If you have a specific table you'd like help with, please provide it, and I can assist you further!
1. **Isolate the Fraction:**
Subtract 2 from both sides of the equation:
\[
\frac{w}{8} + 2 - 2 = 11 - 2
\]
This simplifies to:
\[
\frac{w}{8} = 9
\]
2. **Eliminate the Fraction:**
To eliminate the fraction, multiply both sides by 8:
\[
8 \times \frac{w}{8} = 9 \times 8
\]
This simplifies to:
\[
w = 72
\]
So, the solution to the equation \( \frac{w}{8} + 2 = 11 \) is \( w = 72 \).
### Creating an Equation from a Table
If you have a table of values, you can create an equation that describes the relationship between the input (often \( x \)) and output (often \( y \)). For example, consider the following table of values:
| \( x \) | \( y \) |
|---------|---------|
| 0 | 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
| 4 | 6 |
#### Steps to Create an Equation:
1. **Identify the Pattern:**
In this table, as \( x \) increases by 1, \( y \) increases by 1 as well.
2. **Write the Equation:**
From the observed pattern, we can infer that the relationship is linear. The \( y \)-intercept (the \( y \) value when \( x = 0 \)) is 2. The slope (the rate of change) is 1 (since \( y \) increases by 1 for each increase of 1 in \( x \)).
Therefore, the equation can be expressed as:
\[
y = x + 2
\]
You would simply follow this approach of observing changes in \( x \) and \( y \) to create an equation based on your specific table of values. If you have a specific table you'd like help with, please provide it, and I can assist you further!