Solve. 10/3x + 4/3 = 7 + x/2x
A) x = 1/3
B) x = 17/5x
C) x = 1/5
D) x = 1/6
I can not tell what is numerator and what is denominator
eg
10/(3x) or (10/3)x ???
7 + 1/2 or (7+x)/2 ????
(7+x)/(2x) or [ (7+x)/2 ] x ????
It's 10/(3x) + 4/3 = (7+x)/2x sorry for not making that clear
10/(3x) + 4/3 = (7+x)/2x
20+8x=21+3x
5x=1
x=1/5
To solve the equation (10/3)x + (4/3) = 7 + (x/2x), we can follow these steps:
Step 1: Simplify the equation by finding a common denominator.
The least common denominator (LCD) of 3 and 2x is 6x. So, we multiply each term by 6x:
6x * (10/3)x + 6x * (4/3) = 6x * 7 + 6x * (x/2x)
The equation becomes:
(20x^2/3) + (8x/3) = 42x + 3x
Step 2: Combine like terms.
On the left side, we can add the fractions with the same denominator:
(20x^2/3 + 8x/3) = (28x/3)
On the right side, we can combine the x terms:
(42x + 3x) = (45x)
The equation becomes:
28x/3 = 45x
Step 3: Isolate the variable.
To isolate x, we can multiply both sides of the equation by the reciprocal of the fraction (3/28):
(28x/3) * (3/28) = 45x * (3/28)
The equation simplifies to:
x = (45x * 3) / 28
Step 4: Solve for x.
Now we can multiply and divide to solve for x:
x = (135x) / 28
Divide both sides by x to isolate x:
1 = 135/28
To get x, we need to find the reciprocal of (135/28):
x = 28/135
Simplifying further:
x = 4/19
So, the solution to the equation is x = 4/19.
None of the given options A, B, C, or D is correct.