Final answer:
The algebraic equation 5(x+2) = 6x + 3x - 14 is solved through a step-by-step process involving distribution, combination of like terms, and using the properties of equality to isolate x, which results in the solution x = 6.
Step-by-step explanation:
To solve the equation 5(x+2) = 6x + 3x - 14, we start by applying the Distributive property to the left-hand side:
5x + 10 = 9x - 14
Subtract 5x from both sides, justifying it with the Subtraction property of equality:
10 = 4x - 14
Add 14 to both sides, using the Addition property of equality:
24 = 4x
Finally, divide both sides by 4, as per the Division property of equality, to solve for x:
x = 6
After solving, it's important to check the answer to ensure it makes sense by substituting x back into the original equation. If each side of the equation balances with the value of x, it confirms the solution is reasonable.