solve the inequality. Expiation each step and identify the property used. (n)/(-3)+5>4
(n)/(-3)+5>4
(n)/(-3)+1 > 0
1 > -n/(-3)
1 > n/3
3 > n
or, n < 3
To solve the inequality (n)/(-3) + 5 > 4, we can follow these steps:
Step 1: Subtract 5 from both sides of the inequality. This will help us isolate the variable.
(n)/(-3) + 5 - 5 > 4 - 5
(n)/(-3) > -1
Step 2: Multiply both sides of the inequality by -3. When multiplying or dividing by a negative number, we need to reverse the inequality symbol.
(-3) * (n)/(-3) < -1 * (-3)
n < 3
Therefore, the solution to the inequality (n)/(-3) + 5 > 4 is n < 3.
In this process, we used two properties:
1. Property: Subtracting the same amount from both sides.
Explanation: This property maintains the equality of the inequality while isolating the variable on one side.
2. Property: Multiplying both sides by a negative number.
Explanation: When we multiply or divide by a negative number, the direction of the inequality symbol needs to be reversed to maintain the inequality's truth.