what is the solution to the equation below?

4x + 3 (x - 2) = 8x - (6 + x)

A: infinite solutions

B: no solution

C: x = 6

D: x = -4

3 answers

To solve the equation, we simplify both sides of the equation:

4x + 3(x - 2) = 8x - (6 + x)
4x + 3x - 6 = 8x - 6 - x
7x - 6 = 7x - 6

Now, we notice that both sides of the equation are equal. This means that any value of x will satisfy the equation. Therefore, the equation has infinite solutions.

Therefore, the answer is A: infinite solutions.
actually?
My apologies for the mistake. Let's re-evaluate the equation:

4x + 3 (x - 2) = 8x - (6 + x)

Distributing the 3 on the left side:

4x + 3x - 6 = 8x - 6 - x

Combining like terms:

7x - 6 = 7x - 6

Now, we notice that the variable terms (7x) cancel out on both sides of the equation.

-6 = -6

This is a true statement, which means that the equation is an identity. It implies that any value of x will satisfy the equation. Therefore, the equation has infinite solutions.

Thus, the answer is A: infinite solutions.