Solve
5/2x + 1/4x = 9/4 + x
The solution is x 9/10
Did you omit an = sign?
Show your steps. I don't agree with your statement.
4(5/2x + 1/4x = 9/4 + x)
10x + x =9 + x
11x=9 + x
-x -x
10x = 9
x= 9/10
Your mistake is in the second line. You did not multiply the x on the right side by 4, as you did for the other terms on both sides.
To solve the equation 5/2x + 1/4x = 9/4 + x, we can follow these steps:
Step 1: Start with the given equation: 5/2x + 1/4x = 9/4 + x
Step 2: Find the common denominator for the fractions on the left side of the equation. The common denominator is 4x.
5/2x + (1/4) * (x/1) = 9/4 + (x/1)
Step 3: Simplify the fractions:
(5 * 2)/(2 * 2x) + (x)/(4x) = 9/4 + (x/1)
10/4x + x/4x = 9/4 + (x/1)
10/4x + x/4x = 9/4 + 4x/4x
10/4x + x/4x = (9 + 4x)/4x
Step 4: Combine the fractions:
(10 + x)/(4x) = (9 + 4x)/(4x)
Step 5: Cross-multiply to eliminate the denominators:
(10 + x) * (4x) = (9 + 4x) * (4x)
40x + x^2 = 36x + 16x^2
Step 6: Rearrange the equation and set it equal to zero:
x^2 - 20x = 0
Step 7: Factor out x:
x(x - 20) = 0
Step 8: Set each factor equal to zero and solve for x:
x = 0 or x - 20 = 0
If x = 0, the left side of the equation becomes 0, which does not satisfy the original equation. Therefore, we disregard this solution.
If x - 20 = 0, we solve for x:
x = 20
Therefore, the solution to the equation 5/2x + 1/4x = 9/4 + x is x = 20.