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Solve the inequality. Explain all steps and identify the properties used.
n/-3 + 5 > 4
n / - 3 = - n / 3
- n / 3 + 5 > 4
Multiply both sides by 3.
- n + 15 > 12
Subtract 15 to both sides.
- n > - 3
Multiply both sides by - 1.
When you multiply or divide both sides of an inequality by a negative number, you must change the direction of the inequality sign.
n < 3
To solve the inequality n/-3 + 5 > 4, we need to isolate the variable n.
Step 1: Subtract 5 from both sides of the inequality:
n/-3 + 5 - 5 > 4 - 5
n/-3 > -1
Step 2: Multiply both sides of the inequality by -3 to get rid of the fraction:
-3 * (n/-3) > -1 * (-3)
n > 3
So, the solution to the inequality n/-3 + 5 > 4 is n > 3.
Properties used in the solution:
1. Addition Property of Inequalities: This property allows us to subtract the same value from both sides of an inequality without changing the direction of the inequality.
2. Multiplication Property of Inequalities: This property allows us to multiply both sides of an inequality by the same positive number without changing the direction of the inequality.
To solve the inequality n/-3 + 5 > 4, we will isolate the variable n step-by-step:
Step 1: Subtract 5 from both sides of the inequality.
n/-3 + 5 - 5 > 4 - 5
n/-3 > -1
Step 2: Multiply both sides of the inequality by -3. Since we are multiplying by a negative number, we need to flip the inequality sign.
(-3)(n/-3) < (-1)(-3)
n < 3
The solution to the inequality is n < 3.
Properties used:
1. Addition Property of Inequality: We subtracted 5 from both sides of the inequality to isolate the variable n.
2. Multiplication Property of Inequality:
- Since we multiplied both sides by -3, a negative number, we had to flip the inequality sign.