Question

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

Answer 1

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:
\[
\boxed{-9}
\]