Question

Solve for x: 3|2x - 2| + 6 = 18. (5 points)

a) x = 3, x = -3
b) x = 3, x = -1
c) x = 1, x = -1
d) x = -3, x = 1

Answer 1

To solve the equation 3|2x - 2| + 6 = 18, we can start by subtracting 6 from both sides to isolate the absolute value term. Then, we divide both sides by 3 to get |2x - 2| = 4. By splitting the equation into two cases, we can solve for x and find that the solution is x = 3, x = -1.

Step-by-step explanation:

To solve the equation 3|2x - 2| + 6 = 18, we can start by subtracting 6 from both sides to isolate the absolute value term. This gives us 3|2x - 2| = 12. Then, we divide both sides by 3 to get |2x - 2| = 4.

Next, we can split the equation into two cases. In the first case, 2x - 2 is positive or zero. In the second case, 2x - 2 is negative. In the first case, we can remove the absolute value symbols, resulting in 2x - 2 = 4. Solving this equation gives x = 3. In the second case, we remove the absolute value symbols and flip the sign of the equation, resulting in -(2x - 2) = 4. Solving this equation gives x = -1.

Therefore, the solution to the equation is x = 3, x = -1.