3/4-1/3z=1/4
5/6c-2/3c=1/3
please show step by step
Thanks!
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3/4 - 1/3Z = 1/4
-3/4 -3/4
- 1/3Z = -2/4
* -3 *-3
Z = (-2/4)*-3
Z = 6/4 = 1 & 1/2
Sure, I'd be happy to help you solve the equations step by step. Let's start with the first equation:
3/4 - 1/3z = 1/4
Step 1: To eliminate the fractions, we can multiply the entire equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 12 since it is the lowest number that both 4 and 3 go into evenly.
Multiply every term in the equation by 12:
12 * (3/4) - 12 * (1/3z) = 12 * (1/4)
Simplifying each term, we have:
9 - 4z = 3
Step 2: Next, let's isolate the variable z by moving the constant term to the other side of the equation. In this case, we can do this by subtracting 9 from both sides:
9 - 9 - 4z = 3 - 9
Simplifying, we get:
-4z = -6
Step 3: Now, solve for z by dividing both sides of the equation by -4:
-4z / -4 = -6 / -4
Simplifying, we have:
z = 3/2
Therefore, the solution to the first equation is z = 3/2.
Now, let's move on to the second equation:
5/6c - 2/3c = 1/3
Step 1: Again, we need to find the least common denominator (LCD) of the fractions involved. In this case, the LCD is 6 since it is the lowest number that both 6 and 3 go into evenly.
Multiply every term in the equation by 6:
6 * (5/6c) - 6 * (2/3c) = 6 * (1/3)
Simplifying each term, we have:
5c - 4c = 2
Step 2: Combine like terms by subtracting 4c from 5c:
c = 2
Therefore, the solution to the second equation is c = 2.
I hope that helps! Let me know if you have any further questions.