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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 no solution. The equation has no solution. The equation has one solution: x=1 . The equation has one solution: x equals 1 . The equation has infinite solutions. The equation has infinite solutions. Skip to navigation

1 answer

To solve the equation \( 5(2x+2)−4=2x+6 \), let's simplify both sides step by step.

  1. Start by distributing the 5 on the left side: \[ 5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6 \] So the left side becomes \( 10x + 6 \).

  2. Now rewrite the equation: \[ 10x + 6 = 2x + 6 \]

  3. Next, we'll move \( 2x \) to the left side by subtracting \( 2x \) from both sides: \[ 10x - 2x + 6 = 6 \]

    This simplifies to: \[ 8x + 6 = 6 \]

  4. Now, let's isolate \( 8x \) by subtracting 6 from both sides: \[ 8x = 0 \]

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

We found that \( x = 0 \).

Now we need to determine the nature of the solutions. Here, since we found a specific value for \( x \), the equation has one solution: \( x = 0 \).

So the answer is:

  • The equation has one solution: \( x = 0 \).