Solving One-Step Equations

Solving equations is a large part of mathematics. Once you learn to solve equations, there are a lot of different topics that can be taught. Solving Equations is one of the main topics of Algebra.

To start at the beginning, we will solve one-step equations. They are named as such because it takes you one calculation to get the answer.

The main rule when solving equations is whatever math operation you do to one side of the equation must be done to both sides to keep the equation balanced; or true.

A one-step equation can look like this:
1) 5m = 10
2) 6 + z = 15
3) d - 4 = 12
4) y / 5 = 20

Typically one-step equations can be solved using mental math, as long as you can read an equation. For example, notice that the addition and subtraction problems are easy to identify. #4 is a division problem because the fraction bar means division. #1 is a multiplication problem because there is no +, -, x, or ÷ sign. EVERY TIME there is no operation between two numbers or variables means it's always a multiplication problem.

Before you can start solving an equation you will need to figure out if it's adding, subtracting, multiplying, or dividing. The first step for us to solve an equation is to do the opposite of what was done to the number in the first place.

Rules:
If the variable has been multiplied by a number, we need to divide to solve it.
If the variable has been divided by a number, we need to multiply to solve it.
If the variable has been added to a number, we need to subtract to solve it.
If the variable has been subtracted by a number, we need to add to solve it.

For example: #1
5m = 10
in words: Five times some number, m, equals 10.
Five times two equals ten.
So m = 2 is the answer.

For example: #2
6 + z = 15
in words: six plus some number, z, equals 15.
Six plus 9 equals 15.
So z = 9 is the answer.

For example: #3
d - 4 = 12
in words: some number minus four is twelve.
16 - 4 = 12.
So d = 16 is the answer.

For example: #4
y / 5 = 20
in words: some number, y, divided by five is twenty.
100 ÷ 5 = 20.
So y = 100 is the answer.

Another way to solve equations using mental math is to rewrite the problem without the variable, for people who don't like the alphabet in the equations.

Example: 5 + h = 9
Rewrite it as 5 + ⧠ = 9
Now determine what number goes in the empty box. This will be the answer. This is a useful technique in the beginning to help you learn.

Using an empty box to replace a variable or letter, is often an easier way to start solving equations.

Example 1:
8 + y = 15
Solution: 8 + ⧠ = 15
8 + 7 = 15
y = 7 *Answer

Example 2:
14 - d = 6
Solution: 14 - ⧠ = 6
14 - 8 = 6
d = 8 *Answer

Example 3:
7g = 42
Solution: 7 x ⧠ = 42
7 x 6 = 42
g = 6 *Answer

Example 4:
18/c = 3
Solution: 18 ÷ ⧠ = 3
18 ÷ 6 = 3
c = 6 *Answer

Rules:
If the variable has been multiplied by a number, we need to divide to solve it.
If the variable has been divided by a number, we need to multiply to solve it.
If the variable has been added to a number, we need to subtract to solve it.
If the variable has been subtracted by a number, we need to add to solve it.

Solving equations by hand is somewhat of a method that will soon be outdated. If you go to the store app on your cell phone, you can download apps that can solve the equation for you. All you do is take a still shot of the equation and it automatically solves it for you. Technology and the people who invent it are helping change math in a positive manner.

Let's try some examples: