To determine the number of solutions for the equation \( 5(2x + 2) - 4 = 2x + 6 \), we'll start by simplifying both sides of the equation.
-
Distribute the 5 on the left side: \[ 5(2x + 2) = 10x + 10 \] So, the equation becomes: \[ 10x + 10 - 4 = 2x + 6 \]
-
Simplify the left side further: \[ 10x + 6 = 2x + 6 \]
-
Now, subtract \( 2x \) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
-
Next, subtract 6 from both sides: \[ 8x = 0 \]
-
Finally, divide by 8: \[ x = 0 \]
Since we found a single solution \( x = 0 \), the equation has one solution.
2 answers