Final answer:
The equation 7(x-3) = 4(x + 5) is solved by distributing the multiplication, moving variables to one side, constants to the other, and then isolating x to find that x equals 13.67.
Step-by-step explanation:
To solve for x in the equation 7(x-3) = 4(x + 5), we first distribute the 7 and the 4 into the parentheses:
7x - 21 = 4x + 20
Now, we will eliminate terms to simplify the equation. We do this by moving all the x terms to one side and the numerical values to the opposite side. We subtract 4x from both sides:
7x - 4x - 21 = 20
This simplifies to:
3x - 21 = 20
Next, we add 21 to both sides to isolate the term with x:
3x = 41
Finally, we divide by 3 to solve for x:
x = 41 / 3
x = 13.67
To ensure the solution is reasonable, we can plug x back into the original equation and see if both sides are equal. The solution is correct if both sides match after substituting x with 13.67.