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.

1 answer

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: \(x = 0\).