Questions: Score for Question 1: of 6 points 1. Solve for x. Show each step of the solution. 5.5(6-x)+27=100-2.5(3x+20)

Score for Question 1: of 6 points 1. Solve for x. Show each step of the solution. 5.5(6-x)+27=100-2.5(3x+20)
Transcript text: (Score for Question 1: $\qquad$ of 6 points) 1. Solve for $x$. Show each step of the solution. \[ 5.5(6-x)+27=100-2.5(3 x+20) \] Answer:
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Solution

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Solution Steps

To solve for \( x \) in the given equation, we need to follow these steps:

  1. Distribute the constants inside the parentheses.
  2. Combine like terms on both sides of the equation.
  3. Isolate the variable \( x \) by moving all terms involving \( x \) to one side and constant terms to the other side.
  4. Solve for \( x \).
Step 1: Distribute the Constants

Distribute the constants inside the parentheses: \[ 5.5(6 - x) + 27 = 100 - 2.5(3x + 20) \] \[ 5.5 \cdot 6 - 5.5x + 27 = 100 - 2.5 \cdot 3x - 2.5 \cdot 20 \] \[ 33 - 5.5x + 27 = 100 - 7.5x - 50 \]

Step 2: Combine Like Terms

Combine like terms on both sides of the equation: \[ 60 - 5.5x = 50 - 7.5x \]

Step 3: Isolate the Variable \( x \)

Move all terms involving \( x \) to one side and constant terms to the other side: \[ 60 - 50 = -7.5x + 5.5x \] \[ 10 = -2x \]

Step 4: Solve for \( x \)

Solve for \( x \): \[ x = \frac{10}{-2} \] \[ x = -5 \]

Final Answer

\(\boxed{x = -5}\)

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