Final answer:
To solve the equation 1/2(4x - 12) + 3x = 24, distribute the half, combine like terms, and solve by isolating x to find that x equals 6.
Step-by-step explanation:
To solve the equation 1/2(4x - 12) + 3x = 24, let's first distribute the 1/2 across the parentheses and then simplify the equation:
1/2 × 4x - 1/2 × 12 + 3x = 24
2x - 6 + 3x = 24
Then combine like terms:
2x + 3x - 6 = 24
5x - 6 = 24
Next, add 6 to both sides of the equation to isolate the term with the variable x:
5x - 6 + 6 = 24 + 6
5x = 30
Lastly, divide both sides by 5 to solve for x:
5x/5 = 30/5
x = 6