Solve the following inequality for cc. Write your answer in simplest form.
2, c, minus, 10, is less than, 3, c, minus, 9
2c−10<
3c−9
To solve this inequality, we need to isolate the variable c on one side of the inequality.
Starting with 2c - 10 < 3c - 9, we can first move the c terms to one side by subtracting 2c from both sides:
-10 < c - 9
Next, we can isolate the c term by adding 9 to both sides:
-1 < c
Therefore, the solution to the inequality is: c > -1
To solve the inequality 2c - 10 < 3c - 9 for cc, follow these steps:
Step 1: Start with the given inequality: 2c - 10 < 3c - 9.
Step 2: Subtract 2c from both sides of the inequality to isolate the cc term. This gives: -10 < c - 9.
Step 3: Add 9 to both sides of the inequality to isolate the cc term. This gives: -1 < c.
Therefore, the solution to the inequality 2c - 10 < 3c - 9 in simplest form is c > -1.
To solve the inequality 2c - 10 < 3c - 9 for cc, we need to isolate cc on one side of the inequality symbol (<).
First, let's collect all the cc terms on the left side of the inequality:
2c - 10 < 3c - 9
Now, we can move the 3c term to the left side by subtracting 3c from both sides of the inequality:
2c - 10 - 3c < 3c - 9 - 3c
Simplifying both sides of the inequality gives us:
-1c - 10 < -9
Next, we can simplify the left side further by combining like terms:
-c - 10 < -9
Now, let's isolate the cc term by moving the constant term (-10) to the right side of the inequality by adding 10 to both sides:
-c - 10 + 10 < -9 + 10
Simplifying:
-c < 1
Finally, we need to get rid of the negative sign in front of c. We can multiply both sides of the inequality by -1, but since we are multiplying by a negative number, we also need to reverse the inequality symbol:
(-1)(-c) > 1(-1)
Simplifying:
c > -1
So the solution to the inequality 2c - 10 < 3c - 9 is c > -1.