Solving One Step Equations
Learn how to solve one step equations in 2 easy steps.
There are four things that you must remember when solving any equation AND everything must be mathematically
correct!
Your goal is to get the variable that you are solving for by itself on one side of the equation.
Example: x = _____
To eliminate a term on one side of the equation, you use the opposite mathematical operation.
Whatever you do to one side of the equation, you MUST do to the other side of the equation. This keeps the equation
balanced!
Always check your answer by substituting the value back into the original equation.
Addition equations are pretty easy to solve. Remember that the opposite of addition is subtraction, and
whatever you do to one side, you must do to the other side!
The strategy for getting the variable by itself with a coefficient of 1 involves using opposite operations. For
example, to move something that is added to the other side of the equation, you should subtract. The most
important thing to remember in solving a linear equation is that whatever you do to one side of the equation,
you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value
from the other side. You will see how this works in the examples.
Let's Practice:
i.
Solve
Remember the goal is to have the variable by itself on one side of the equation. In this problem, that means moving the 5
to the other side of the equation. Since the 5 is added to the variable, we move it to the other side of the equation by
subtracting 5. However, if we subtract 5 from the left side of the equation, we MUST also subtract 5 from the right side.
ii.
Solve
It does not matter that the variable in this equation is on the right side of the equation. The position of the variable is not
an issue. Remember that the goal is to have the variable on one side by itself. It does not matter which side.
To get the variable by itself, we need to add 3 to both sides.
iii.
Solve
The variable in this equation is already on one side of the equation by itself. There is no need to add or subtract anything
to both sides. However, the number in front of the variable is not 1. The -3 that is in front of the variable indicates
multiplication of -3 by x. The opposite operation of multiplication is division. So we will divide both sides by -3.
You should take note of the different ways of writing the answer. In the example, we divided by -3, yet wrote the answer
with the negative in front of the entire fraction, not just the 3. Each of the following fractions all mean the same thing.
iv.
Solve
The variable in this equation is already on one side by itself, but it is divided by 3. To get rid of the 3 that is attached to
the variable by division, we will perform the opposite operation which is multiplication. Notice that our variable can be
any letter. It does not always have to be x.
Solving Two-Step Algebra Equations
 Always remove the constant first using addition or subtraction.
 Your second step will be to remove any coefficients or divisors using multiplication or division.