Solve
5/2X + 1/4X = 5/4 +X
I will assume you meant
(5/2)X + (1/4)X = (5/4) + X
multiply each term by 4
10x + x = 5 + 4x
I am sure you can take it from here
from here would you combined 4x-10x=-6x
then it would show x=5+-6x and then you would go +6 to both sides to get 6x=5 and then divide to get your answer would this be correct?
NO
10x + x = 5 + 4x
11x - 4x = 5
7x = 5
x = 5/7
Thank you for your help!
To solve the equation 5/2X + 1/4X = 5/4 + X, we need to simplify the equation and solve for X.
Step 1: Get rid of the fractions by finding a common denominator.
The denominators in the equation are 2, 4, and 1. The least common multiple (LCM) of 2, 4, and 1 is 4. Therefore, we need to multiply each term in the equation by 4 to clear the fractions.
4 * (5/2X) + 4 * (1/4X) = 4 * (5/4) + 4 * X
Step 2: Simplify each term by canceling out the denominators.
(20/2X) + (4/4X) = (20/4) + 4X
Step 3: Further simplify the equation.
10/X + 1/X = 5/1 + 4X
Step 4: Combine the like terms on the left side of the equation.
(10 + 1)/X = 5 + 4X
11/X = 5 + 4X
Step 5: Multiply through by the common denominator to eliminate fractions.
11 = 5X + 4X^2
Step 6: Rearrange the equation to form a quadratic equation.
0 = 4X^2 + 5X - 11
Step 7: Solve the quadratic equation.
To solve the quadratic equation, you can use different methods such as factoring, completing the square, or using the quadratic formula. If factoring is not possible, you can use the quadratic formula.
The quadratic formula is X = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 4, b = 5, and c = -11.
Plugging in the values into the quadratic formula, we get:
X = (-(5) ± √((5^2) - 4(4)(-11))) / (2(4))
Calculating inside the square root:
X = (-5 ± √(25 + 176)) / 8
X = (-5 ± √(201)) / 8
Therefore, the solutions to the equation are:
X = (-5 + √(201)) / 8
and
X = (-5 - √(201)) / 8