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2(x−1)+3x−5=

−17

1 answer

To solve the equation \( 2(x - 1) + 3x - 5 = -17 \), let's first simplify the left side.

  1. Distribute the \( 2 \) in \( 2(x - 1) \): \[ 2x - 2 \]

  2. Substitute this back into the equation: \[ 2x - 2 + 3x - 5 = -17 \]

  3. Combine like terms: \[ (2x + 3x) + (-2 - 5) = -17 \] which simplifies to: \[ 5x - 7 = -17 \]

  4. Next, add \( 7 \) to both sides: \[ 5x - 7 + 7 = -17 + 7 \] Simplifying gives: \[ 5x = -10 \]

  5. Now, divide both sides by \( 5 \): \[ x = \frac{-10}{5} \] Thus, we have: \[ x = -2 \]

So the solution to the equation \( 2(x - 1) + 3x - 5 = -17 \) is \( \boxed{-2} \).