5/4x + 1/8x = 3/8 + x =
X =
I read that as
(5/4)x + (1/8)x
= (11/8)x
or
if you meant ...
5/(4x) + 1/(8x), then
= 10/(8x) + 1/(8x)
= 11/(8x)
or
if you have an equation
(5/4)x + (1/8)x = 3/8 + x
I would multiply each term by 8 and it becomes a very simple equation.
or ....
The Xs are in the numerator or the de-
nominator
If they are in the numerator, (5/4)x =
5x/4 , and (1/8)x = x/8.
5x/4 + x/8 = 3/8 + x
5x/4 + x/8 - x = 3/8,
Multiply both sides by 8:
10x + x - 8x = 3,
3x = 3,
x = 1.
If the Xs are in the denominator,
5/4x + 1/8x = 3/8 + x.
Multiply both sides by 8x:
1O + 1 = 3x + 8x^2,
8x^2 + 3x - 11 = 0
Factor using A*C method:
A*C = 8*-11 = -88,
8x^2 +11x-8x -11 = 0
Group the 4 terms into factorable pairs
(8x^2 - 8x) + (11x - 11) = 0,
Factor 8x from the 1st pair and
11 from the 2nd 2 pair:
8x(x - 1) + 11(x - 1) = 0,
Factor (x - 1) from each term:
(x - 1) (8x + 11) = 0,
x - 1 = 0, x = 1; 8x + 11 = 0, x = -11/8. S0lution: X = 1, AND X = -11/8.
To solve this equation for x, we need to first simplify the expression on both sides of the equation by combining like terms.
On the left side of the equation, we have (5/4)x + (1/8)x. To combine these terms, we need to find a common denominator for 4 and 8, which is 8. So, we can rewrite the expression as:
(5/4)x + (1/8)x = (10/8)x + (1/8)x
Now, we can add the coefficients of x together:
(10/8)x + (1/8)x = (11/8)x
So, the left side of the equation simplifies to (11/8)x.
On the right side of the equation, we have 3/8 + x. To combine these terms, we need to find a common denominator for 8 and 1, which is 8. So, we can rewrite the expression as:
3/8 + x = 3/8 + (8/8)x
Now, we can add the coefficients of x together:
3/8 + (8/8)x = (3/8) + (8/8)x
So, the right side of the equation simplifies to (3/8) + (8/8)x.
Therefore, the equation is:
(11/8)x = (3/8) + (8/8)x
To solve for x, we want to isolate the x term on one side of the equation. We can do this by subtracting (8/8)x from both sides:
(11/8)x - (8/8)x = (3/8) + (8/8)x - (8/8)x
Simplifying the left side, we have:
(3/8) = (3/8)x
To solve for x, we can now divide both sides of the equation by (3/8):
(3/8) / (3/8) = (3/8)x / (3/8)
The left side simplifies to 1:
1 = x
So, the value of x is 1.