5/3 x + 1/3 x = 5x +32/3 +7/3x
No question. Are you being asked to solve for x?
5/3x*3+1/3X*3=5x*3+32/3*3+7/3x*3
5x+x=15x+32+7x
6x=22x+32
-32=22x-6x
-32=16x
x=-2
To solve the equation 5/3x + 1/3x = 5x + 32/3 + 7/3x, we need to simplify both sides of the equation and move all the terms containing x to one side.
Starting with the left side of the equation:
5/3x + 1/3x can be combined by adding the coefficients of x.
5/3x + 1/3x = (5/3 + 1/3)x
The denominators are the same, so we can add the numerators.
(5/3 + 1/3)x = (6/3)x
Simplifying further:
(6/3)x = 2x
Now, let's look at the right side of the equation:
5x + 32/3 + 7/3x can also be simplified by combining like terms.
First, let's add 5x and 7/3x together:
5x + 7/3x = (15/3)x + (7/3)x
The denominators are the same, so we can add the numerators.
(15/3)x + (7/3)x = (22/3)x
Now, we add this result to 32/3:
(22/3)x + 32/3 = (22/3)x + (32/3)
Now, we have simplified both sides of the equation:
2x = (22/3)x + (32/3)
To solve for x, we need to isolate the variable on one side of the equation. We can achieve this by moving the term (22/3)x from the right side to the left side:
2x - (22/3)x = 32/3
To subtract the fractions with different denominators, we need to find a common denominator, which is 3 in this case.
Multiplying the first fraction by 3/3 gives:
(6/3)x - (22/3)x = 32/3
Now, we can subtract the numerators:
(-16/3)x = 32/3
To solve for x, we need to isolate it. We can do this by multiplying both sides by the reciprocal of -16/3, which is -3/16:
((-3/16) * -16/3)x = (32/3) * (-3/16)
The -16/3 and 3/16 cancel out on the left side, leaving x:
x = (32/3) * (-3/16)
To multiply fractions, we multiply the numerators and multiply the denominators:
x = (32 * -3) / (3 * 16)
Simplifying the numerator and denominator:
x = (-96) / 48
We can simplify further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 48:
x = -2
Therefore, the solution to the equation 5/3x + 1/3x = 5x + 32/3 + 7/3x is x = -2.