Solving Inequalities: -2 3x - 8 10

Understanding how to solve inequalities is a fundamental concept in algebra. In this article, we will walk you through the process of solving the inequality -2 3x - 8 10 step by step. By the end, you will be able to confidently solve similar inequalities on your own.

Understanding the Inequality

Our goal is to find the range of values for x that satisfy the inequality -2 3x - 8 10. This can be thought of as the inequality being true for values of x that make the expression 3x - 8 lie between -2 and 10. We will break down the process into manageable steps.

Solving the Inequality

Let's begin by writing out the inequality for clarity:

-2 3x - 8 10

The first step in solving this inequality is to isolate the term containing x. To do this, we will add 8 to all parts of the inequality. This will eliminate the constant term -8 on the left side:

-2 8 3x - 8 8 10 8

Simplifying the expression, we get:

6 3x 18

The next step is to divide every part of the inequality by 3 to solve for x:

6/3 3x/3 18/3

This simplifies to:

2 x 6

Thus, the solution to the inequality -2 3x - 8 10 is that x must lie between 2 and 6, exclusive of each.

Conclusion

Solving inequalities involves a few key steps: isolating the variable, performing the same operation on all parts of the inequality, and simplifying. By following these steps, you can solve a wide range of inequalities. Remember, the goal is to find the range of values for the variable that satisfy the inequality.

Key Points for Solving Inequalities

Add or subtract the same number from all parts of the inequality to isolate the variable term. Multiply or divide all parts of the inequality by the same positive number to simplify the inequality further. Remember to reverse the inequality sign if you multiply or divide by a negative number.

Practice these steps with various inequalities to gain confidence and proficiency in solving them. If you need more practice or have questions, feel free to reach out to a tutor or use online resources for further assistance.

Tags: inequalities, algebra, solving inequalities