Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the inequality. Explain all steps and identify the properties used.
3a−4≤5
3a−4≤5
3a≤9
now divide by 3
To solve the inequality 3a - 4 ≤ 5, follow these steps:
Step 1: Add 4 to both sides of the inequality to isolate the variable.
3a - 4 + 4 ≤ 5 + 4
3a ≤ 9
Step 2: Divide both sides of the inequality by 3 to solve for 'a'.
(3a) / 3 ≤ 9 / 3
a ≤ 3
So, the solution to the inequality is a ≤ 3.
Properties used:
1. Addition Property of Inequality: Adding the same term to both sides of an inequality does not change the inequality.
2. Transitive Property of Inequality: If a ≤ b and b ≤ c, then a ≤ c.
3. Division Property of Inequality: Dividing both sides of an inequality by a positive number does not change the inequality.