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Solve for x: 8x - 5 = 3x + 20.

x = __

3 answers

To solve the equation \( 8x - 5 = 3x + 20 \), we can start by isolating the variable \( x \).

  1. Subtract \( 3x \) from both sides: \[ 8x - 3x - 5 = 20 \] This simplifies to: \[ 5x - 5 = 20 \]

  2. Next, add \( 5 \) to both sides: \[ 5x - 5 + 5 = 20 + 5 \] This simplifies to: \[ 5x = 25 \]

  3. Finally, divide both sides by \( 5 \): \[ x = \frac{25}{5} \] Thus, \[ x = 5 \]

The solution is \( x = 5 \).

are you sure this is correct

Yes, let's double-check the calculation step by step to confirm the solution is correct.

Starting with the original equation: \[ 8x - 5 = 3x + 20 \]

  1. Subtract \( 3x \) from both sides: \[ 8x - 3x - 5 = 20 \] This simplifies to: \[ 5x - 5 = 20 \]

  2. Now add \( 5 \) to both sides: \[ 5x - 5 + 5 = 20 + 5 \] This simplifies to: \[ 5x = 25 \]

  3. Finally, divide both sides by \( 5 \): \[ x = \frac{25}{5} \] Thus, this gives: \[ x = 5 \]

To verify, let's plug \( x = 5 \) back into the original equation: Left-hand side: \[ 8(5) - 5 = 40 - 5 = 35 \] Right-hand side: \[ 3(5) + 20 = 15 + 20 = 35 \]

Since both sides equal \( 35 \), the solution \( x = 5 \) is correct.