Solve the equation, if possible(answer or no solution);
n-10=5/6n-7-1/3n
Assuming just fractions, meaning
n-10 = 5/6 n - 7 - 1/3 n
n - 5/6 n + 1/3 n = 3
n(1 - 5/6 + 1/3) = 3
1/2 n = 3
n = 6
Check:
6-10 = 5/6 (6) - 7 - 1/3 (6)
-4 = 5-7-2
yes
To solve the equation, let's simplify and rearrange it step by step.
Starting with the given equation:
n - 10 = 5/6n - 7 - 1/3n
First, let's simplify the fractions on the right side of the equation:
n - 10 = (5/6 - 1/3)n - 7
Now, let's find the common denominator for the fractions:
n - 10 = (5/6 - 2/6)n - 7
Simplifying further:
n - 10 = (3/6)n - 7
n - 10 = (1/2)n - 7
Next, let's eliminate the fractions by multiplying the entire equation by 2 to clear the denominators:
2(n - 10) = 2(1/2)n - 2(7)
2n - 20 = n - 14
Moving all the n terms to one side and the constants to the other side:
2n - n = -14 + 20
n = 6
Therefore, the solution to the equation is n = 6.
To solve the equation, we will begin by simplifying the equation by combining like terms.
n - 10 = 5/6n - 7 - 1/3n
First, let's deal with the fractions. To simplify, we need a common denominator, which in this case is 6.
n - 10 = (5/6)n - (7*6/6) - (1/3)n
n - 10 = (5/6)n - 42/6 - (1/3)n
Now, let's simplify further by getting rid of the fractions:
n - 10 = (5/6)n - 7 - (1/3)n
Multiplying every term by 6 to eliminate the fractions:
6n - 60 = 5n - 42 - 2n
Now, combine like terms:
6n - 5n + 2n = -42 + 60
3n = 18
Finally, we isolate the variable by dividing both sides by 3:
(3n)/3 = 18/3
n = 6
Therefore, the solution to the equation is n = 6.