To solve the equation \( 5(2x+2)-4=2x+6 \), let's first simplify both sides.
-
Distribute the 5 on the left side: \[ 5(2x) + 5(2) - 4 = 10x + 10 - 4 \] This simplifies to: \[ 10x + 6 \]
-
Now, rewrite the equation: \[ 10x + 6 = 2x + 6 \]
-
Next, subtract \( 2x \) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
-
Now, subtract 6 from both sides: \[ 8x = 0 \]
-
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.