Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?
Inequalities are one of the most important topics which are extensively used 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, -8x + 4 > 5 - 3x.
Let's understand the solution in detail.
To solve the inequality –4(2x – 1) > 5 – 3x, we follow the below steps:
- First, open the brackets: -8x + 4 > 5 - 3x
- Next, rearrange the variables and constants: -8x + 3x > 5 - 4
- Next, perform the addition or subtraction operations: -5x > 1
- Next, divide both the sides by 5 to get the final result: -5x/5 > 1/5 ⇒ x < -1/5
Hence, the final solution of the inequality given is x < -0.2.