1/2a-5=1/3a-1 please show me how to set this problem up and solve it
1. Multiply both sides of Eq. by 6.
2.Subtract 2a from both sides of Eq.
3. Add 30 to each side of Eq.
4. Solve for a.
For this type of problem, try to get just the variable on one side and just the numbers on the other side.
(1/2)a - 5 = (1/3)a - 1
Add 5 to both sides to get rid of the number on the left.
(1/2)a - 5 + 5 = (1/3)a - 1 + 5
combining...
(1/2)a = (1/3)a + 4
Now subtract (1/3)a from both sides to get rid of the variable on the right side:
(1/2)a - (1/3)a = (1/3)a - (1/3)a + 4
using a common denominator of 6...
(3/6)a - (2/6)a = 4
combining...
(1/6)a = 4
multiply both sides by 6
a = 24
Substitute 24 for a in the original problem to check.
I know both tutors above solved the problem correctly according to the way you typed it, but I have a sneaking suspicion that you meant to type
1/(2a-5) = 1/(3a-1)
cross-multiply to get
3a - 1 = 2a - 5
a = -4
if the equation is as you typed it, then ignore my reply.
To solve the equation 1/2a - 5 = 1/3a - 1, you need to eliminate the fractions and isolate the variable 'a'. Here's how you set up and solve the problem:
Step 1: Clear the fractions by finding a common denominator.
To get rid of the fractions, we'll find a common denominator for both sides. The least common denominator (LCD) between 2 and 3 is 6. Multiply each term by 6 to achieve this:
6 * (1/2a) - 6 * 5 = 6 * (1/3a) - 6 * 1
Simplifying this equation gives us:
3/a - 30 = 2/a - 6
Step 2: Combine like terms.
Next, combine the terms with 'a' on one side and the constant terms on the other side. In this case, we'll move the '2/a' term to the right side and the '30' constant term to the left side:
3/a - 2/a = -6 + 30
Simplifying this equation gives us:
1/a = 24
Step 3: Isolate the variable.
To solve for 'a', we'll isolate it by multiplying both sides of the equation by 'a':
a * (1/a) = 24 * a
Simplifying this equation gives us:
1 = 24a
Finally, divide both sides of the equation by 24 to solve for 'a':
a = 1/24
So the solution to the equation 1/2a - 5 = 1/3a - 1 is a = 1/24.