1/5 + 3/25x - 3 = 2/3/5
Solve
2/3/5 is an unusual expression. Is there a typo? If not, we have
3/25 x = 2/3/5 + 3 - 1/5
3/25 x = 2/15 + 3 - 1/5
3/25 x = 46/15
x = 46/15 * 25/3 = 46*5/3 = 230/3
To solve the equation 1/5 + 3/25x - 3 = 2/3/5, we need to combine like terms and isolate the variable x.
Step 1: Simplify the Fractions
To make the calculations easier, let's first convert all the fractions to have the same denominator.
The common denominator for 5, 25, and 3/5 is 25. So, we can rewrite the equation as follows:
(1/5) + (3/25)x - 3 = (2/3) / (5/1)
Step 2: Simplify the Equation
Now, let's simplify the right side of the equation.
To divide a fraction by another fraction, we flip the second fraction and multiply:
(1/5) + (3/25)x - 3 = (2/3) * (1/5/1)
Next, let's simplify the right side of the equation by multiplying the fractions:
(1/5) + (3/25)x - 3 = (2/3) * (1 * 1/5)
Simplifying further:
(1/5) + (3/25)x - 3 = (2/3) * (1/5)
Now, let's multiply across:
(1/5) + (3/25)x - 3 = (2/15)
Step 3: Combine Like Terms
Now, we need to combine like terms on both sides of the equation.
On the left side, we have (1/5) and -3.
(1/5) - 3 + (3/25)x = (2/15)
To make it easier to combine fractions, we can express -3 as -15/5:
(1/5) + (-15/5) + (3/25)x = (2/15)
Combining the fractions:
(-14/5) + (3/25)x = (2/15)
Step 4: Isolate the Variable
To isolate the variable x, we need to get rid of the constant term on the left side.
We can do this by adding 14/5 to both sides of the equation:
(-14/5) + (3/25)x + (14/5) = (2/15) + (14/5)
Simplifying:
(3/25)x = (2/15) + (14/5)
Now, we need to find a common denominator for (2/15) and (14/5).
The least common multiple (LCM) of 15 and 5 is 15. So, let's rewrite the right side of the equation with a common denominator:
(3/25)x = (2/15) * (1 * 5/5) + (14/5) * (3/3)
Simplifying further:
(3/25)x = (10/15) + (42/15)
Combining the fractions:
(3/25)x = (52/15)
Step 5: Solve for x
To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides by (25/3) (the reciprocal of 3/25):
(3/25)x * (25/3) = (52/15) * (25/3)
Simplifying:
x = (52/15) * (25/3) / (3/25)
Now, let's multiply across:
x = (52 * 25) / (15 * 3) * (25/3) / (3/25)
Simplifying further:
x = (1300/45) * (25/3) / (3/25)
Now, let's multiply across:
x = (1300 * 25) / (45 * 3) * (25/3) / (3/25)
Simplifying further:
x = (32500/135) * (25/3) / (3/25)
Finally, let's multiply across:
x = (32500 * 25) / (135 * 3) * (25/3) / (3/25)
Simplifying further:
x = 812500 / 1215
Now, we can simplify this fraction:
x ≈ 669.9596
So, the solution to the equation is approximately x = 669.9596.