Question

Solve for a to determine if the equation has one, none, or infinite solutions.

5(2x + 2) - 7x = 3x + 6 (1 point)

The equation has one solution: x = 6

The equation has no solution.

The equation has infinite solutions.

The equation has one solution: x = 10

Answer 1

To solve for a, we need to simplify the equation and collect like terms.

Starting with the given equation:
5(2x + 2) - 7x = 3x + 6

First, distribute 5 to the terms within the parentheses:
10x + 10 - 7x = 3x + 6

Next, combine like terms by subtracting 10x from both sides:
10 - 7x = 3x + 6 - 10x

Simplifying further:
10 - 7x = -7x + 6

We can see that the variable term (-7x) is on both sides of the equation. This means that when we subtract -7x from both sides to isolate the constant term, it will eliminate x completely. So, we are left with:
10 = 6

This is a contradiction since 10 cannot equal 6. Therefore, there are no values of a that will make this equation true. Therefore, the equation has no solution.