# Linear Equations in One Variable Worksheets

We all know that linear equations are equations that often used to give a mathematical recipe for a line that can be drawn on a coordinate graph. We are going to focus a unique version of these equations called a linear equation in one variable. These math statements are unique because there is only a single variable present, as their name implies. As a result, there is only one possible solution to these types of equations. They take on the standard form of skeleton equation ax + b = 0. As we can see here, a represents the coefficient, x represents the variable, and b represents the constant term. This value is all equal to zero. These worksheets and lessons teach students to understand all the parts of linear equations.

### Aligned Standard: Grade 8 Expressions and Equations - 8.EE.C.7a

- How Many Solutions Step-by-Step Lesson- How many solutions can an equation have? You decide in this one.
- Guided Lesson - Have you ever heard of visualizing equations with models? Now you have.
- Guided Lesson Explanation - I provide simple solutions that are more for vocal learners.
- Independent Practice - Solve for x, solve word problem equations, and solve for x including product formulas.
- Matching Worksheet - A nice round up of all the skills learned for this section.
- Absolute Value Equations Five Pack - Equations that have an absolute on one side. How can you go wrong?
- Solving Fractional Equations Five Pack - Remember to combine your like terms.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

How many solutions are there, solve for x, and story based algebra problems.

- Homework 1 - We know that if solving an equation yields a statement that is false, like 7=11, then the equation has no solution.
- Homework 2 - Solve equation algebraically.
- Homework 3 - 15 more than two times of a certain number is six more than 3 times of that number. Whatâ€™s the number?

### Practice Worksheets

We took all the skills from the homework and mixed them up into these sheets.

- Practice 1 - Seven less than a number that is more than four times divided by 6 is seventy. What was just described?
- Practice 2 - Solve for b: 28 = 4(b+12)
- Practice 3 - Seven times a number plus one is eight.

### Math Skill Quizzes

By request, I threw an absolute value problem into the first quiz.

- Quiz 1 - 40 more than three times of a certain number is twenty more than 5 times of that number. What's the number?
- Quiz 2 - Solve for the variable in each case.
- Quiz 3 - What number is being described in each problem?

### The Steps of Solving Linear Equations in One Variable

There are several general steps we can take to solve and satisfy the missing variable in these types of equations. Here are all the steps that we recommend taking:

**Step 1) Separate the Variable and Constants** - In most cases this can be done through simple operations (addition, subtraction, division, multiplication) that are just the opposite of what is present.

**Step 2) Simplify Any Constants** - Get everything in the simplest terms possible.

**Step 3) Set Apart the Variable** - This can normally be done by multiplying or dividing it on both sides of the equal sign.

**Step 4) Reduce** - It is always good form to write everything in the simplest terms possible.

### What Do the Variables Stand for in Linear Equations?

Linear equations are equation that are used to describe a line on a coordinate graph. The first part of the term itself **line**ar gives this away. It is also a good way to remember this. Algebraic equations are made up of numbers and variables (letters), with one arithmetic operation that needs to be solved. The standard form of these equations can be stated as ax +by = c. The variables a, b, and c represent coefficients or constant quantities. The x and y indicate the x and y position of point on graphs. In most cases, if you know one of the positions (x or y) you can just plug them into the equation to find the other.

Before you get on to solving the equations, you might as well have a clear and basic understanding of what variables are. When we see algebraic equations, there are letters such as x, y, z, a, b, m, d. These variables imply that the value of these variables is not known. Usually, when there is a variable in the equation, you must find the value of the variable using the arithmetic operation that is given.