Questions: Solve the equation below. 7(x-3)-2=20x-101

Solve the equation below. 7(x-3)-2=20x-101
Transcript text: Solve the equation below. \[ 7(x-3)-2=20 x-101 \]
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Solution

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Solution Steps

To solve the equation \( 7(x-3) - 2 = 20x - 101 \), we need to follow these steps:

  1. Expand the left-hand side of the equation.
  2. Combine like terms on both sides.
  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: Expand the Left-Hand Side

Expand the left-hand side of the equation \( 7(x-3) - 2 \): \[ 7(x-3) - 2 = 7x - 21 - 2 = 7x - 23 \]

Step 2: Combine Like Terms

Rewrite the equation with the expanded left-hand side: \[ 7x - 23 = 20x - 101 \]

Step 3: Isolate the Variable \( x \)

Move all terms involving \( x \) to one side and constant terms to the other side: \[ 7x - 20x = -101 + 23 \] \[ -13x = -78 \]

Step 4: Solve for \( x \)

Divide both sides by \(-13\): \[ x = \frac{-78}{-13} = 6 \]

Final Answer

\[ \boxed{x = 6} \]

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