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## Introduction

An equation represents a mathematical problem that has already been put together.  Each equation contains a problem and an answer separated by an equal sign.  When you first began doing math, you simplified expressions, which only took into account the problem.  Now you will look at equations, where there are two parts (problem and answer).  The table below compares expressions and equations.

Expression                                      Equation

5 × 4                                               5a = 0

6 × 11                                             6b = 66

(-3)(5) + 6                                       -3c + 6 = -9

Each expression above represents the same information as the equation to its right.  For example, the expression 5  × 4 simplifies to 20.  The equation 5a = 20 can be solved and the solution would be a = 4.

Pretend for a moment that you are picking a number between 1 and 10.  You then double that number and get a result of 14.  What was your original number?

This situation can be modeled by the equation 2x = 14.

The letter “x” in the above equation is called a variable.  A variable is simply a letter or symbol that stands for a number.  When you are confronted with an equation, you find you answer by solving it.

The equation 2x = 14 can be solved quickly and easily.  In fact, you can probably do it in your head.  However, the equations that you will see throughout the next few lessons will get more and more difficult, so it is important to understand and use the correct steps.

## Lesson

One step equations are the simplest type of equation to solve.  As the name states, only one step is required to find the answer.  The only necessary step is to look at the operation that is being performed on the variable and do the opposite operation.

To gain a greater understanding of equations, observe the thinking behind finding the value of the missing numbers:

To find the missing number, think about what number makes a total of 8 when it is added with 5.  In your mind, you are actually doing subtraction to find the answer.  The difference of 8 and 5 is 3.

This missing number can be found by identifying a number that equals 24 when it is multiplied by 4.  In your mind, you are actually doing division to find the answer.  The quotient of (24 ÷ 4) equals 6.

In both of the above examples, you use the opposite of the operation that is shown to find the solution to the problem.

Most math teachers require you to show work on these problems.  That is because equations will soon become larger and more complex.  To give yourself the best chance of solving equations in the future, start today by learning how to show work and by showing the work yourself each time you do a problem.

The following one-step equations can be solved by doing the opposite of the operation.

Since you are adding 12 to the variable on the left side, you can find the answer by subtracting 12 from each side.

Note that the 12’s being subtracted are colored blue.  In the examples, blue represents a work step while black is used in equation steps.

You are multiplying the variable t by 5 on the left side, so you will divide both sides by 5 to solve the equation.

The work step in this problem is "divide each side by five."  Even if you can do the problem in your head, showing the work step can help you explain your work and prove  that you know what you are doing to solve the equation.

The red line in each problem is used to divide each equation into a right side and a left side.  The purpose of dividing the problem into a left side and a right side is to make it easier tell that you are doing the same thing to each side.

So basically one step equations can be solved by adding, subtracting, multiplying, or dividing the same number on both sides.

## Try It

Solve the following equations:

1)  x + 11 = 39

2)  r - 18 = -35

3)  -7m = -56

4)  12h = 84

5)  b/3 = -8

6)  z + (-16) = -35

1)  x + 11 = 39

Solution:

2)  r – 18 = -35

Solution:

3)  -7m = -56

Solution:

4)  12h = 84

Solution:

5)  b/3 = -8

Solution:

6)  z + (-16) = -35

Solution: