m+1
---
4
+
5
--
6
=
2m-1
----
12
3m+3 10 2m-1
____ + __ = _____
12 12 12
Now that all of your denominators are the same the problem becomes 3m+3+10=2m-1
3m+13=2m-1
m+13=-1
m=-14
thank you jen
To solve the given equation, we will follow these steps:
Step 1: Simplify each part of the equation separately.
Let's start with the first equation: (m + 1) / 4.
Step 2: Solve the first equation.
To simplify (m + 1) / 4, divide both the numerator and the denominator by 1:
(m + 1) ÷ 1 = m + 1
4 ÷ 1 = 4
Therefore, the simplified form of (m + 1) / 4 is (m + 1) / 4.
Now let's move on to the second equation: 5 / 6.
Step 3: Solve the second equation.
Since 5 is not divisible by 6, 5 / 6 is already in its simplest form.
Lastly, let's solve the third equation: (2m - 1) / 12.
Step 4: Solve the third equation.
To simplify (2m - 1) / 12, divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 2m - 1 and 12 is 1 (since there are no common factors other than 1).
Dividing both the numerator and the denominator by 1, we get:
(2m - 1) ÷ 1 = 2m - 1
12 ÷ 1 = 12
Therefore, the simplified form of (2m - 1) / 12 is (2m - 1) / 12.
Step 5: Combine the simplified equations.
Now we have:
(m + 1) / 4 + 5 / 6 = (2m - 1) / 12
To combine the left side of the equation, we need to find a common denominator for 4 and 6.
Step 6: Find a common denominator.
The least common multiple (LCM) of 4 and 6 is 12.
Step 7: Convert the fractions to have the same denominator.
Multiplying the first fraction (m + 1) / 4 by 3/3 and the second fraction 5 / 6 by 2/2 (to make the denominators 12), we get:
3(m + 1) / 12 + 10 / 12 = (2m - 1) / 12
Simplifying further, we have:
(3m + 3 + 10) / 12 = (2m - 1) / 12
Step 8: Combine like terms.
Combining the like terms on the left side, we get:
(3m + 13) / 12 = (2m - 1) / 12
Step 9: Set the numerators equal to each other.
Since the denominators are the same, we can set the numerators equal:
3m + 13 = 2m - 1
Step 10: Solve for m.
Let's isolate the variable m on one side by subtracting 2m from both sides of the equation:
3m - 2m + 13 = 2m - 2m - 1
m + 13 = -1
To isolate m, subtract 13 from both sides of the equation:
m + 13 - 13 = -1 - 13
m = -14
Therefore, the solution to the equation (m + 1) / 4 + 5 / 6 = (2m - 1) / 12 is m = -14.