Question

Solve for x determine if the equation has one none or infinite solutions
5(2x+2)-7x=3x+6
The equation has no Solution
The equation has one solution x = 6
The equation has one solution x = 10
The equation has infinite solutions

Answer 1

To solve the equation \( 5(2x+2) - 7x = 3x + 6 \), we will first distribute the \( 5 \) on the left side:

\[
5 \cdot 2x + 5 \cdot 2 - 7x = 3x + 6
\]

This simplifies to:

\[
10x + 10 - 7x = 3x + 6
\]

Now, combine like terms on the left:

\[
(10x - 7x) + 10 = 3x + 6
\]

This simplifies to:

\[
3x + 10 = 3x + 6
\]

Next, we can isolate the variable \( x \) by subtracting \( 3x \) from both sides:

\[
10 = 6
\]

This statement is false, which indicates that there are **no solutions** to the equation.

Thus, the answer is:

**The equation has no solution.**