Final Answer:
The value of x in the equation (2)/(x-12) + (x-10)/(5) = 18 is x = 14.
Step-by-step explanation:
To solve for x in the given equation, we'll follow these steps:
Obtain a common denominator for the fractions on the left side.
Combine the fractions.
Set the combined fraction equal to 18 and solve for x.
Equation: (2)/(x-12) + (x-10)/(5) = 18
Common denominator: 5(x-12)
(2 * 5)/(5(x-12)) + (x-10)/(5) = 18
Combine the fractions:
(10)/(5(x-12)) + (x-10)/(5) = 18
Set equal to 18 and solve for x:
(10 + (x-10))/(5(x-12)) = 18
x/(5(x-12)) = 18
Cross-multiply and solve:
x = 14
Therefore, x = 14 is the solution to the equation.