## Solving Equations and Inequalities

#### Aligned To Common Core Standard:

**Grade 6 Expressions and Equations** - 6.EE.B.5

What Is the Difference Between Equations and Inequalities? Though sounding more like each other, Equations and Inequalities are different. Let's find out what is the difference between the two. An equation is an expression that focuses on maintaining the equality of the two expressions. Inequalities, on the other hand, are mathematical expressions that use signs or symbols in the equation such as > for higher than or < for lesser to show that an expression is lesser than or more than the other. Following is the example of an equation and inequality: 2x^2 + 3y + 1 = 0, 2x + 10 > 0. An equation displays the equality of two variables, while an inequality demonstrates the inequality of two variables. Though both equations and inequality are solved through different solutions, an equation gives only one answer while they can provide several answers. An equation uses variables like x and y while an inequality uses symbols such as (less than) < and (higher than) >.

### Printable Worksheets And Lessons

- Solving an Inequality
Step-by-step Lesson- This is a great follow up to the visual
inequalities that we saw in early standards. If you approach these problems with base logic, they will make sense.

- Guided Lesson - Determine
the truth of a series of inequalities. Use all the information that is available to you.

- Guided Lesson Explanation
-This was actually refreshing to write. The number of times I have
explained this to students flashed before me. I'm just going to
print this for them.

- Practice Worksheet - This
is a multiple choice sheet that has you find the value of the variable
that will make the statement true.

- Solving Equations Five
Pack - The problems might be a bit too spread out. I did this
to mimic a test question I saw years ago.

- Solving Inequalities
by Adding and Subtracting Five Pack- If they understand that
sum and differences are inverses of one another, they are set.

- Solving Inequalities by Multiplying and Dividing Five Pack - The quotient is set up a number ways in different problems. I went with the standard version here.
- Absolute Value Inequalities Five Pack - Nothing real fancy here. Just solve for the variable of the inequality.
- Matching Worksheet - Find the missing parts or solutions to the inequalities. Use the choices to drive your solution.

#### Homework Sheets

My students would always refer to these problems as "Plug and Play!"

- Homework 1 - Is r = 9 a solution to the inequality below? r < 5
- Homework 2 - Which value for B would make the inequality true?
- Homework 3 - Which value for z would make the inequality z false?

#### Practice Worksheets

Algebra skills start popping here. It might be a bit advanced for some learners.

- Practice 1 - Is u = 10 a solution to the inequality: u < 23
- Practice 2 - Find the value of x.
- Practice 3 - Solve the inequalities by adding and/or subtracting.

#### Math Skill Quizzes

The last quiz is very algebra loaded, just for a reference.

- Quiz 1 - Which value for t would make the inequality true?
- Quiz 2 - Which value for m would make the inequality m false?
- Quiz 3 - Solve the inequalities by adding and subtracting.

### The Approach to Finding Solutions for These Types of Problems

Regardless of which of these types of problems you are tasked with finding a solution for the basic tactics are very similar. The general aim is getting the unknown variable (which is usually x) by itself. To make it read correctly we often try to isolate that variable to the left of the equals or inequality symbol. The first thing to do is to always simply any operations that are present. From there general rules apply for both types of problems. You can perform operations (add, subtract, multiply, or divide) on positive numbers as long as you do it to both sides of the problem. There is a concern when working negative numbers with inequalities, if you multiply or divide both sides of an inequality with a negative number the inequality symbol will be flipped in the opposite direction from which it was presented. One way to check that your inequality is stated correctly is to make sure that the sign always points to the smaller value. Remember that we always want to represent our variable on the left-hand side of the expression. When working with equations, we can just rearrange the sides so that the variable is on the left by flipping it. With inequalities we can do the same thing, by the symbol flips direction if we rearrange it. Fractions often scare students that are new to this skill. The easiest way to tackle these problems is to just multiply all sides by the denominator to make all the values whole.