Solving Equations and Inequalities Worksheets
There are many different ways to compose math statements which imply a value or a method for determining an unknown value or quantity. When these statements indicate that two things are equal, usually through the use of an equal symbol (=), we call this statement an equation. When a math statement is composed that compares two values showing that one side is greater or lesser than the other side, we call this an inequality. When you are solving equations and inequalities, you take the same basic approach. When you do one thing to a one side of the comparison symbol, you must do the same to the other side. The only real difference comes into play when we are working with negative numbers with inequalities. If you multiple or divide by a negative number when solving an inequality, the comparison symbol flips direction (greater than becomes less than and vice versa. These worksheets will give you some experience with solving both types of math statements.
Aligned Standard: Grade 6 Expressions and Equations - 6.EE.B.5
- 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.
- Answer Keys - These are for all the unlocked materials above.
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?
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.
What Is the Difference Between Equations and Inequalities?
Though most students often confuse this, equations and inequalities are different. Due to the fact that you often process to solve them in the very same manner, this where everyone attributes them to being the same thing. 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. As a result equations always include an equal sign (=). Inequalities, on the other hand, are mathematical expressions that use comparison 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:
Equation: 2x2 + 3y + 1 = 0, Inequality: 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 inequalities can provide several answers or a scale of answers. Inequalities often give you an idea of where the answer lies, but nothing exact. Both of them can use multiple types of variables such as (x, y) to define unknown values.
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.