Question

Solve for x to determine if the equation has one, none, or infinite solutions.
4(2x+2)-7x=3x+6

Answer 1

To solve the equation, we can start by distributing the 4 to the terms inside the parentheses:

8x + 8 - 7x = 3x + 6

Next, combine like terms on both sides of the equation:

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

Simplifying further, we have:

x + 8 = 3x + 6

Now, we can isolate the x term on one side by subtracting x from both sides:

8 = 2x + 6

Subtracting 6 from both sides:

2 = 2x

Finally, we can solve for x by dividing both sides by 2:

1 = x

Therefore, the solution to the equation is x = 1.

Since we found one unique solution for x, the equation has exactly one solution.