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 determine if the expressions 2(x - 1) + 18 and 6(x + 3) - 4x - 6 are equal, we will simplify both sides of the equation and see if they are equivalent.
First, we simplify the left side of the equation:
2(x - 1) + 18 = 2x - 2 + 18 = 2x + 16.
Next, we simplify the right side of the equation:
6(x + 3) - 4x - 6 = 6x + 18 - 4x - 6 = 6x - 4x + 12 = 2x + 12.
By simplifying both sides of the equation, we find that 2(x - 1) + 18 is equal to 6(x + 3) - 4x - 6 if and only if the left side, 2x + 16, is equal to the right side, 2x + 12.
Since both sides of the equation are equal to 2x + (the same constant), the two expressions are indeed equivalent.