Question

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x + 2) - 4 = 2x + 6 (1 point)
. The equation has one solution:
x = 1.
• The equation has infinite solutions.
• The equation has no solution.
. The equation has one solution:
x = 0.

Answer 1

Let's solve the equation step by step:

The original equation is:
\[ 5(2x + 2) - 4 = 2x + 6 \]

First, distribute the 5 on the left side:
\[ 10x + 10 - 4 = 2x + 6 \]

Now simplify the left side:
\[ 10x + 6 = 2x + 6 \]

Next, we'll move all the terms involving \(x\) to one side and the constant terms to the other side. Subtract \(2x\) from both sides:
\[ 10x - 2x + 6 = 6 \]
\[ 8x + 6 = 6 \]

Now subtract 6 from both sides:
\[ 8x = 0 \]

Finally, divide both sides by 8:
\[ x = 0 \]

Now we evaluate the result:

- Since we found a specific value \(x = 0\), the equation has **one solution**.

Thus, the correct conclusion from the given options is:
• The equation has one solution: \(x = 0\).