Solving 1-Variable Inequalities
Have you ever wondered what heights are included when an amusement park says you must be at least 42 inches tall to go on a ride?
What is a 1 - variable inequality? Check out the first graphic in the fundamental Problem Solving: Writing 1-Variable Inequalities!
What does it mean to solve a 1-variable inequality?
First, what is an inequality? An inequality is anytime two expressions are being compared to each other. Remember, if two expressions are compared with only an equal sign, then you are dealing with an equation and not an inequality.
What does it mean to solve a 1.pdfWhat are properties and concepts I may need to use when solving 1-variable inequalities?
First, solving 1-variable inequalities is very similar to solving 1-variable equations. You may need to use any of the following properties/concepts: order of operations, distributive property, combining like terms, reverse order of operations, and inverse operations.
If you need a refresher on how to use the above properties/concepts when solving equations check out the fundamental Solving Complex 1-Variable Equations!
A new concept to inequalities is what happens when multiplying and dividing by a negative. When dealing with an equation (or two expressions that are equal), there is nothing to really think about when multiplying or dividing by negative values. But it’s very different with inequalities.
Multiplying and Dividing Inequalities by a Negative Value
Multiplying and Dividing Inequalities by a Negative Value.pdfWhat is a solution to an inequality?
A solution to an inequality is going to be a range of values. The value you solve for, such as -2, in the above example, is simply a boundary point. In the example above, the boundary point: -2, is not included in the solution.
Why are some boundary points included and some other boundary points not included?
For a boundary point to be included, the inequality must include the equal bar under the less than or greater than sign. For a boundary point to not be included, the inequality will not include the equal bar and simply be a greater than or less than sign.
What is a solution to an inequality.pdfHow do you solve a 1-variable inequality?
Example 1: variable on one side of the inequality
Example 1.pdfExample 2: variable on both sides of the inequality
Example 2.pdfExample 3: dividing by a negative
Example 3.pdfExample 4: multiplying by a negative
Example 4.pdfExample 5: complex inequality
Example 5.pdfDid you notice that solving a 1-variable inequality is very similar to solving a 1-variable equation? If you struggled with isolating the variable using inverse operations to solve a 1-variable inequality check out the fundamentals: Solving 1-Variable Equations: Variable on One Side of the Equation; and Solving 1-Variable Equations: Variable on Both Sides of the Equation!
If you need more help with combining like terms and the distributive property while solving 1-variable inequalities, check out the fundamental: Solving Complex 1-Variable Equations!
Why do we learn how to solve a 1-variable inequality?
Why do we learn how to solve a 1.pdfWhat’s next? To see a 1-variable inequality in action, check out the fundamental Problem Solving: Writing 1-Variable Inequalities!
Did you notice? The not equal to sign was not included in solving 1-variable inequalities but you will find it in the fundamentals: Types of Solutions: Linear 1-Variable Equations and systems of equations - coming soon!
