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Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?

Combine like terms, 3 and 5, on the right side of the equation.
Distribute 2 to (x + 6) and 3 to (x – 4).
Distribute 2 to x on the left side of the equation and 3 to x on the right side of the equation.
Apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.

1 answer

A reasonable first step to solve the equation \( 2(x + 6) = 3(x - 4) + 5 \) is to distribute. Specifically, you can either:

  1. Distribute 2 to \( (x + 6) \) on the left side of the equation, which gives you \( 2x + 12 \).
  2. Or distribute 3 to \( (x - 4) \) on the right side of the equation, which gives you \( 3x - 12 \).

Either distribution will help simplify the equation and move you towards solving it.

Thus, one good first step is: Distribute 2 to (x + 6) and 3 to (x – 4).