Solve for x

Question

x
to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
5
(
2
x
+
2
)
−
7
x
=
3
x
+
6

Answer 1

To solve for x, let's simplify the equation step by step:

1) Distribute the 5 to both terms inside the parentheses:
10x + 10 - 7x = 3x + 6

2) Combine like terms on the left side of the equation:
(10x - 7x) + 10 = 3x + 6
3x + 10 = 3x + 6

3) Subtract 3x from both sides to eliminate the x term on the right side:
3x - 3x + 10 = 3x - 3x + 6
10 = 6

4) Since 10 is not equal to 6, the equation is inconsistent and has no solution.