What is a correct first step in solving the inequality –4(3 – 5x) ≥ –6x + 9?
Inequalities are very important topics that are used in the calculations related to problems in algebra, trigonometry, and calculus problems.
Answer: The first step in solving the given inequality is to use the distributive property and open the brackets, that is, -12 + 20x ≥ -6x + 9.
Let's understand the solution step by step.
To solve the inequality –4(3 – 5x) ≥ –6x + 9, we follow the below steps:
- First, open the brackets and perform the multiplication: -12 + 20x ≥ -6x + 9
- Next, rearrange the variables and constants in the inequality: 20x + 6x ≥ 9 + 12
- Next, perform the addition operations on both sides: 26x ≥ 21
- Next, divide both sides by 26 to get the final answer: 26x/26 ≥ 21/26 ⇒ x ≥ 21/26
Hence, the final solution of the inequality given is x ≥ 21/26.