Solve each equation and check your solution. 6x-5x+2=12-19

1 answer

Let's solve the equation \( 6x - 5x + 2 = 12 - 19 \).

  1. First, simplify both sides of the equation.

    On the left side: \[ 6x - 5x + 2 = (6 - 5)x + 2 = 1x + 2 = x + 2 \]

    On the right side: \[ 12 - 19 = -7 \]

    So the equation becomes: \[ x + 2 = -7 \]

  2. Now, isolate \( x \) by subtracting 2 from both sides: \[ x = -7 - 2 \] \[ x = -9 \]

Now, let's check the solution by substituting \( x = -9 \) back into the original equation:

Original equation: \[ 6x - 5x + 2 = 12 - 19 \]

Substituting \( x = -9 \): \[ 6(-9) - 5(-9) + 2 = 12 - 19 \]

Calculating the left side: \[ 6(-9) = -54 \] \[ -5(-9) = 45 \] Now summarize: \[ -54 + 45 + 2 = -54 + 47 = -7 \]

Calculating the right side: \[ 12 - 19 = -7 \]

Since both sides equal \(-7\), our solution \( x = -9 \) is correct.

Thus, the final answer is: \[ \boxed{-9} \]