Question

Solving Linear Equations Unit Test 18 of 1918 of 19 Items Question Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−4=2x+6 (1 point) Responses The equation has one solution: x=0 . The equation has one solution: x equals 0 . The equation has one solution: x=1 . The equation has one solution: x equals 1 . The equation has no solution. The equation has no solution. The equation has infinite solutions.

Answer 1

To solve the equation \( 5(2x + 2) - 4 = 2x + 6 \), we'll first distribute the 5 on the left side:

\[
5(2x + 2) = 10x + 10
\]

Now substitute that back into the equation:

\[
10x + 10 - 4 = 2x + 6
\]

Simplify the left side:

\[
10x + 6 = 2x + 6
\]

Next, we'll subtract \(2x\) from both sides:

\[
10x - 2x + 6 = 6
\]

This simplifies to:

\[
8x + 6 = 6
\]

Now, subtract 6 from both sides:

\[
8x = 0
\]

Finally, divide by 8:

\[
x = 0
\]

Now we can determine the nature of the solution. Since we found a unique value of \(x\), there is **one solution** for the equation.

So, the answer is:
**The equation has one solution: x = 0.** (You can choose either response with "x=0" or "x equals 0" as they mean the same.)