Final answer:
To solve for x in the equation 8x + 14 = 6(x + 4), follow these steps: distribute the 6, combine like terms, isolate x by subtracting and dividing, and check the solution.
Step-by-step explanation:
To solve for x in the equation 8x + 14 = 6(x + 4), we can follow these steps:
- First, distribute the 6 to the terms inside the parentheses: 8x + 14 = 6x + 24.
- Next, combine like terms by subtracting 6x from both sides: 8x - 6x + 14 = 6x - 6x + 24, simplifying to 2x + 14 = 24.
- Then, subtract 14 from both sides: 2x + 14 - 14 = 24 - 14, simplifying to 2x = 10.
- Finally, divide both sides by 2 to isolate x: 2x/2 = 10/2, simplifying to x = 5.
To justify our solution:
- Substituting x = 5 back into the original equation, 8(5) + 14 = 6(5 + 4) simplifies to 54 = 54, which is true.
- We can also check our solution by graphing the equation and verifying that the x-coordinate of the point of intersection is indeed x = 5.