i need some help figuring out this question
2 3/5c - 1/2 > 3/10
To solve the inequality 2 3/5c - 1/2 > 3/10, we need to isolate the variable c.
Step 1: Simplify both sides of the inequality:
2 3/5c - 1/2 > 3/10
Rewrite the mixed number 2 3/5 as an improper fraction: 2 3/5 = (2 * 5 + 3)/5 = 13/5
Now the inequality becomes: (13/5)c - 1/2 > 3/10
Step 2: Get rid of the fractions by multiplying both sides of the inequality by the least common multiple (LCM) of the denominators. The LCM of 5, 2, and 10 is 10:
10 * ((13/5)c - 1/2) > 10 * (3/10)
This simplifies to: 2(13c - 5) > 3
Step 3: Distribute and simplify:
26c - 10 > 3
Step 4: Move the constant term (-10) to the other side of the inequality:
26c > 3 + 10
26c > 13
Step 5: Divide both sides by the coefficient of c (26) to solve for c:
c > 13/26
Therefore, the solution to the inequality 2 3/5c - 1/2 > 3/10 is c > 13/26.