To solve the equation \( \frac{w}{8} + 2 = 11 \), you can follow these steps:
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Isolate the Fraction: Subtract 2 from both sides of the equation: \[ \frac{w}{8} + 2 - 2 = 11 - 2 \] This simplifies to: \[ \frac{w}{8} = 9 \]
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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:
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Identify the Pattern: In this table, as \( x \) increases by 1, \( y \) increases by 1 as well.
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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!