6/7s-3/4=4/5-1/7s+1/6
6/7s-3/4=4/5-1/7s+1/6
6/7s + 1/7s = 3/4 + 4/5 + 1/6
s = 45/60 + 48/60 + 10/60
s = 103/60 = 1 43/60
Check my math.
the denominators are 7,4,5,7, and 6
so the LCD is 420
so multiply each term by 420
360s - 315 = 336 - 60s + 70
360s+60s = 336 + 70 + 315
420s = 721
s = 721/420
s = 103/60
To solve the equation 6/7s - 3/4 = 4/5 - 1/7s + 1/6, we can follow these steps:
Step 1: Combine like terms on each side of the equation.
On the left side, we have 6/7s - 3/4.
On the right side, we have 4/5 - 1/7s + 1/6.
Step 2: Convert all the fractions to have a common denominator.
The common denominator for the fractions 7, 4, 5, and 6 is 420.
So, we need to convert all the fractions to have a denominator of 420.
On the left side, we can multiply 6/7s by (60/60) to get:
(6/7s) * (60/60) = (360/420)s
On the left side, we can multiply 3/4 by (105/105) to get:
(3/4) * (105/105) = (315/420)
So, the left side becomes (360/420)s - (315/420).
On the right side, we can multiply 4/5 by (84/84) to get:
(4/5) * (84/84) = (336/420)
On the right side, we can multiply 1/7s by (60/60) to get:
(1/7s) * (60/60) = (60/420)s
On the right side, we can multiply 1/6 by (70/70) to get:
(1/6) * (70/70) = (70/420)
So, the right side becomes (336/420) - (60/420)s + (70/420).
Step 3: Simplify the equation.
Now that we have the equation as (360/420)s - (315/420) = (336/420) - (60/420)s + (70/420), we can simplify it further.
First, combine like terms on each side:
On the left side: (360/420)s - (315/420) = (45/420)s - (315/420).
On the right side: (336/420) - (60/420)s + (70/420) = (406/420) - (60/420)s.
Now, combine the two sides of the equation:
(45/420)s - (315/420) = (406/420) - (60/420)s.
Step 4: Continue simplifying.
To simplify the equation further, we can multiply every term by 420 to clear out the fractions:
(420 * (45/420)s) - (420 * (315/420)) = (420 * (406/420)) - (420 * (60/420)s).
This simplifies to:
45s - 315 = 406 - 60s.
Step 5: Solve for 's'.
Now, we can solve the equation for 's'.
Add 60s to both sides: 45s + 60s - 315 = 406 - 60s + 60s.
Simplify: 105s - 315 = 406.
Add 315 to both sides: 105s - 315 + 315 = 406 + 315.
Simplify: 105s = 721.
Divide both sides by 105: (105s)/105 = 721/105.
Simplify: s = 721/105.
Therefore, the solution to the equation 6/7s - 3/4 = 4/5 - 1/7s + 1/6 is s = 721/105.