Solving inequalities is one of the fundamental skills that you need to master in math. An inequality is simply a statement that tells you that one value is greater than or less than another value. To solve an inequality means finding the values that make the statement true.

In this blog post, we’re going to go through an example problem and show you how to solve it using step-by-step methods. The problem we’re going to tackle is:

4x – 12 ≤ 16 + 8x

The first step in solving any inequality is to simplify both sides of the equation. In this case, we can simplify it by combining like terms, so we get:

-4x – 12 ≤ 16

Next, we’ll add 12 to both sides of the equation to isolate the variable term. This gives us:

-4x ≤ 28

Finally, we’ll divide both sides of the equation by -4. But, we have to remember that if we divide by a negative number, we need to flip the inequality sign, so we get:

x ≥ -7

Therefore, the solution set for this inequality is all values of x greater than or equal to -7. We can represent this solution set on a number line as a shaded region to the right of -7.

In conclusion, solving inequalities requires some algebraic manipulation and understanding of mathematical concepts. By following a series of steps, you can find the solution set for a given inequality. Remember to always simplify both sides of the equation first, isolate the variable term, and then find the values for the variable that meet the conditions of the inequality. With practice, you’ll be able to solve more complex inequalities with ease.