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Solve for x to determine if the equation has one none or infinite solution.

5(2×+2)-4=2×+6

1 answer

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

  1. Distribute the 5 on the left side: \[ 5(2x) + 5(2) - 4 = 10x + 10 - 4 \] This simplifies to: \[ 10x + 6 \]

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

  3. Next, subtract \( 2x \) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]

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

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

Now, let's check the solutions to determine whether the equation has one, none, or infinite solutions:

  • Since we found one specific value for \( x \) (which is \( x = 0 \)), the equation has one solution.