Question

equation for x.
$-12 + 7x - 5x = 4 - 3x + 2$
as an improper fraction, if necessary.

Explanation:

Step1: Combine like terms on both sides

On the left side, combine the \(x\)-terms: \(7x - 5x = 2x\), so the left side becomes \(-12 + 2x\).
On the right side, combine the constant terms: \(4 + 2 = 6\), so the right side becomes \(6 - 3x\).
Now the equation is \(-12 + 2x = 6 - 3x\).

Step2: Add \(3x\) to both sides

Adding \(3x\) to both sides to get all \(x\)-terms on the left:
\(-12 + 2x + 3x = 6 - 3x + 3x\)
Simplify: \(-12 + 5x = 6\).

Step3: Add 12 to both sides

Adding 12 to both sides to isolate the term with \(x\):
\(-12 + 5x + 12 = 6 + 12\)
Simplify: \(5x = 18\).

Step4: Divide both sides by 5

Divide both sides by 5 to solve for \(x\):
\(x = \frac{18}{5}\).

Answer:

\(x = \frac{18}{5}\)