is 2(x - 1) + 18 equal to 6( x + 3) - 4x - 6? Use algebra to find your answer. Show your work and explain your answer
To solve this equation, we will simplify both sides of the equation and see if they are equal.
First, let's simplify the left side of the equation:
2(x - 1) + 18 = 2x - 2 + 18 = 2x + 16.
Next, let's simplify the right side of the equation:
6(x + 3) - 4x - 6 = 6x + 18 - 4x - 6 = 2x + 12.
Now, we will compare both sides:
2x + 16 = 2x + 12.
Since the x terms cancel out, we are left with:
16 = 12.
Since we have a contradiction here (16 is not equal to 12), the equation is not true for any value of x. Therefore, the original equation 2(x - 1) + 18 = 6(x + 3) - 4x - 6 does not hold.