Questions: Twice the sum of -2 and a number is the same as the number decreased by 7/4. Find the number.

Twice the sum of -2 and a number is the same as the number decreased by 7/4. Find the number.
Transcript text: Twice the sum of -2 and a number is the same as the number decreased by $\frac{7}{4}$. Find the number.
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Solution

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Solution Steps

To solve the problem, we need to translate the given statement into a mathematical equation and then solve for the unknown number.

  1. Identify the unknown number and represent it with a variable, say \( x \).
  2. Translate "Twice the sum of -2 and a number" into an algebraic expression: \( 2(-2 + x) \).
  3. Translate "the number decreased by \( \frac{7}{4} \)" into an algebraic expression: \( x - \frac{7}{4} \).
  4. Set the two expressions equal to each other to form the equation: \( 2(-2 + x) = x - \frac{7}{4} \).
  5. Solve the equation for \( x \).
Step 1: Define the Variable and Translate the Statement

Let \( x \) be the unknown number. The problem states that twice the sum of \(-2\) and the number is the same as the number decreased by \( \frac{7}{4} \).

Step 2: Form the Equation

Translate the statement into an equation: \[ 2(-2 + x) = x - \frac{7}{4} \]

Step 3: Simplify the Equation

Simplify both sides of the equation: \[ 2(-2 + x) = 2x - 4 \] \[ x - \frac{7}{4} = x - 1.75 \]

Step 4: Solve for \( x \)

Set the simplified expressions equal to each other and solve for \( x \): \[ 2x - 4 = x - 1.75 \] Subtract \( x \) from both sides: \[ x - 4 = -1.75 \] Add 4 to both sides: \[ x = 2.25 \]

Final Answer

\[ \boxed{x = \frac{9}{4}} \]

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