I need to make sure this is correct.
5/2x+1/4x=11/4+x
4(5/2x+1/4x=11/4+x)
cancel, left with 10x+1x=11+x
11x=11+x
11x-x=11
10x=11
x=11/10
To check if your solution is correct, you can substitute the value of x back into the original equation and see if both sides are equal.
Original equation: 5/(2x) + 1/(4x) = 11/(4 + x)
Substituting x = 11/10:
5/(2 * (11/10)) + 1/(4 * (11/10)) = 11/(4 + (11/10))
Simplifying:
5/(22/10) + 1/(44/10) = 11/(40/10 + 11/10)
5/(22/10) + 1/(44/10) = 11/(51/10)
Now, let's simplify further. To add fractions, we need to have the same denominator.
5/(22/10) + 1/(44/10) = 11/(51/10)
5 * (10/22) + 1 * (10/44) = 11 * (10/51)
50/22 + 10/44 = 110/51
Now, let's find a common denominator for the fractions on the left side:
50/22 + 10/44
(50 * 2)/(22 * 2) + 10/44
100/44 + 10/44
(100 + 10)/44
110/44
Simplifying the fraction:
110/44 = 55/22
So, on the left side, we have 55/22.
Now, let's simplify the fraction on the right side:
11/(51/10)
11 * (10/51)
110/51
So, on the right side, we have 110/51.
Since 55/22 is equal to 110/51, your solution is correct.