Solving inequalities can be a daunting task, especially when you are dealing with complex equations. However, with the right tools and approach, it is possible to solve them efficiently and accurately. In this post, we will explore the first steps for solving the inequality -4(3-5x) ≥ -6x + 9.

Step 1: Simplify the expression

The first step in solving this inequality is to simplify the expression on both sides of the equation. We can start by simplifying the left-hand side of the equation:

-4(3-5x) = -12 + 20x

Now, let’s simplify the right-hand side of the equation:

-6x + 9 = 9 – 6x

So, the simplified inequality looks like this:

-12 + 20x ≥ 9 – 6x

Step 2: Isolate the variable

Next, we want to isolate the variable to one side of the inequality. We can do this by adding 6x to both sides of the equation:

-12 + 20x + 6x ≥ 9

Simplifying the equation further, we get:

26x ≥ 21

Step 3: Solve for x

Finally, we can solve for x by dividing both sides of the equation by 26:

x ≥ 21/26

Therefore, the solution to the inequality -4(3-5x) ≥ -6x + 9 is x ≥ 21/26.

In conclusion, solving inequalities requires careful attention to detail and a methodical approach. By simplifying the expression, isolating the variable, and solving for x, we can determine the solution to an inequality. With practice, you can increase your proficiency in solving inequalities and tackle more challenging equations.