solve the inequality. explain each step and identify the property used for each step.
5z >_ -75
5z >_ -75
Divide both sides by 5.
z >_ -15
To solve the inequality 5z ≥ -75, we can follow these steps:
Step 1: Divide both sides of the inequality by 5.
Since the coefficient of z is 5, we can divide both sides of the inequality by 5 to isolate z.
(5z)/5 ≥ (-75)/5
This simplifies to z ≥ -15.
Property Used: Division Property of Inequalities. According to this property, if we divide both sides of an inequality by a positive number, the direction of the inequality remains the same.
Step 2: Simplify the inequality.
We simplify the inequality z ≥ -15.
Property Used: There isn't a specific property used in this step. It is more of an application of keeping the inequality in its simplest form.
So, the solution to the inequality 5z ≥ -75 is z ≥ -15.
To solve the inequality 5z ≥ -75, follow these steps:
Step 1: Divide both sides of the inequality by 5.
5z/5 ≥ -75/5
z ≥ -15
Property used: Division Property of Inequality
Explanation: Dividing both sides of the inequality by 5 ensures that the inequality remains true.
Step 2: Simplify the result.
z ≥ -15
Property used: Simplification
Explanation: There are no further simplifications required since z ≥ -15 is already in its simplest form.
In summary, the solution to the inequality 5z ≥ -75 is z ≥ -15.