Let's denote the unknown number as \( x \).
According to the problem, we need to translate the statement into an equation. The statement says:
"Two times the sum of a number and 24" can be written as: \[ 2(x + 24) \]
The phrase "equals the difference of 76 and that same number" can be expressed as: \[ 76 - x \]
Putting it all together, we set up the equation: \[ 2(x + 24) = 76 - x \]
Now, we can simplify and solve the equation.
Expanding the left side: \[ 2x + 48 = 76 - x \]
Next, we add \( x \) to both sides to get all \( x \) terms on one side: \[ 2x + x + 48 = 76 \] \[ 3x + 48 = 76 \]
Now, subtract 48 from both sides: \[ 3x = 76 - 48 \] \[ 3x = 28 \]
Finally, divide by 3: \[ x = \frac{28}{3} \]
Thus, the equation that satisfies the parameters is: \[ 2(x + 24) = 76 - x \]
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