i need some help figuring out this question
2 3/5c - 1/2 > 3/10
combine like terms and divide by 2
To solve the inequality 2 3/5c - 1/2 > 3/10, we need to combine like terms and then divide by 2.
First, let's simplify the left side of the inequality by combining the whole number and fraction.
2 3/5 can be written as an improper fraction: 2 * 5 + 3 = 13/5.
So, the inequality becomes (13/5)c - 1/2 > 3/10.
Next, we can find a common denominator to simplify the inequality further. The common denominator of 5 and 2 is 10.
Multiplying the numerator and denominator of 13/5 by 2, we get (26/10)c - 1/2 > 3/10.
Our new inequality is (26/10)c - 1/2 > 3/10.
Now, let's combine the fractions on the left side.
(26/10)c - 1/2 can be written with a common denominator of 10: (26c - 5)/10 - 1/2 > 3/10.
Combine the numerator: (26c - 5 - 5)/10 > 3/10.
Simplifying further, we have (26c - 10)/10 > 3/10.
Next, we can simplify by dividing both sides of the inequality by 10.
(26c - 10)/10 > 3/10
This becomes (26c - 10) > (3).
Now, we can solve for c by isolating the variable:
Add 10 to both sides of the inequality:
26c - 10 + 10 > 3 + 10
This simplifies to:
26c > 13
Finally, divide both sides of the inequality by 26 to isolate c:
26c/26 > 13/26
Which simplifies to:
c > 13/26
Therefore, the solution to the inequality 2 3/5c - 1/2 > 3/10, after combining like terms and dividing by 2, is c > 13/26.