How do you know whether an inequality, such as this,|2c-5|<9, is "and" or "or".
if it's less than it's "and", if it's greater than it's "or".
thanks
To determine whether an inequality like |2c-5|<9 (where |2c-5| represents the absolute value of the expression 2c-5) is an "and" or "or" inequality, you need to consider the two possible cases separately.
1. AND Inequality:
If you have an "and" inequality, both conditions must be true simultaneously. In the case of |2c-5|<9, it means that the inequality is satisfied when both of the following conditions are met:
- 2c-5 is less than 9
- 2c-5 is greater than -9 (the negative version of 9)
2. OR Inequality:
In an "or" inequality, at least one of the conditions needs to be true. In the case of |2c-5|<9, it means that the inequality is satisfied when either of the following conditions is met:
- 2c-5 is less than 9
- 2c-5 is greater than -9 (the negative version of 9)
To determine whether it is an "and" or "or" inequality, you need to consider whether both conditions must be satisfied simultaneously or if it's enough for just either one to be satisfied.
Let's solve the inequality to find out the answer:
First, we consider the case where 2c-5 is less than 9:
2c-5 < 9
Adding 5 to both sides, we get:
2c < 14
Dividing by 2, we find:
c < 7
Now, let's consider the case where 2c-5 is greater than -9:
2c-5 > -9
Adding 5 to both sides, we get:
2c > -4
Dividing by 2, we find:
c > -2
By analyzing the conditions, we observe that both conditions can be satisfied simultaneously. Therefore, in this case, the inequality |2c-5|<9 is an "AND" inequality, meaning that both conditions must be met for the inequality to hold. To represent this as a combined inequality, we write:
-2 < c < 7