Solve for z 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 = 0 The equation has infinite solutions. The equation has one solution: x = 1 The equation has no solution.

Answer 1

To determine the number of solutions for the equation \(5(2x + 2) - 4 = 2x + 6\), we will simplify and solve it step by step.

1. Start by simplifying the left side: \[ 5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6 \] So, the equation now is: \[ 10x + 6 = 2x + 6 \]

2. Next, let's isolate the variable \(x\) by subtracting \(2x\) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]

3. Subtract 6 from both sides: \[ 8x = 0 \]

4. Finally, divide by 8: \[ x = 0 \]

Now let's consider the types of solutions:

• If \(x = 0\) is the only solution, the equation has one solution.

To summarize, the equation \(5(2x + 2) - 4 = 2x + 6\) has one solution, \(x = 0\).