Multi-step linear inequalities

Multi-step linear inequalities
Description
Exercise Name:	Multi-step linear inequalities
Math Missions:	Algebra basics Math Mission, Mathematics I Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems:	1

The Multi-step linear inequalities exercise appears under the Algebra basics Math Mission, Mathematics I Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise practices solving linear inequalities with multiple instances of the variable and numerical quantities.

Types of Problems

There is one type of problem in this exercise:

1. Solve the inequality: This problem provides a linear inequality. The student is asked to use the properties of inequalities to isolate the variable and use the manipulative to correctly state the inequality.

   

   Solve the inequality

Strategies

Knowledge of the properties of inequality and comfort with the notation are needed to perform this exercise accurately and efficiently.

1. The manipulative requires the variable to always be on the left.
2. Multiplying or dividing an inequality causes the inequality symbol to flip. This is because multiplying by a negative has the geometric effect of reflecting numbers on a one-dimensional number line over the origin.

Real-life Applications

1. Inequalities are much more useful then equation in real-life because of the imprecise nature of the world. Good estimates become more powerful than exact answers.
2. For most people, in order to get their license they have to be at least 16. So, they can write this as an inequality. ${x}$ is the age of a person who wants to drive. In this case ${x}$ has to be greater than or equal to 16.
3. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.