i need some help figuring out this question
2 3/5c - 1/2 > 3/10
3/5x2 - 1/2 > 3/10 x=2
To solve this inequality, we need to isolate the variable "c" on one side of the inequality sign. Here are the steps:
1. Let's start by getting rid of the fraction on both sides of the inequality. To do this, we can multiply each term by the reciprocal of the coefficient of the fraction.
The reciprocal of 3/5 is 5/3, so we multiply both sides of the inequality by 5/3:
(2 3/5c - 1/2) * (5/3) > (3/10) * (5/3)
2. Simplifying each term:
For the left side of the inequality:
- The term 2 times 5/3 gives us 10/3c.
- The term 3/5c times 5/3 gives us (3 * 5)/(5 * 3)c, which simplifies to 1c or c.
For the right side of the inequality:
- The term 3/10 times 5/3 gives us (3 * 5)/(10 * 3), which simplifies to 1/2.
Our inequality becomes:
10/3c - 1/2 > 1/2
3. Let's move the constant term (-1/2) to the other side of the inequality by adding 1/2 to both sides:
10/3c - 1/2 + 1/2 > 1/2 + 1/2
Simplifying:
10/3c > 1
4. Next, we want to isolate the variable "c" on one side of the inequality, so let's multiply both sides by the reciprocal of the coefficient of "c."
The reciprocal of 10/3 is 3/10, so we multiply both sides of the inequality by 3/10:
(10/3c) * (3/10) > (1) * (3/10)
5. Simplifying each term:
For the left side of the inequality:
- The term 10/3c times 3/10 gives us (10 * 3)/(3 * 10)c, which simplifies to 1c or c.
For the right side of the inequality:
- The term 1 times 3/10 gives us 3/10.
Our inequality becomes:
c > 3/10
Therefore, the solution to the given inequality is c > 3/10.