Tips For Solving Multi-Step Equations

Can you do the two-step equations? No, it's not a dance but a description of solving a type of equation in mathematics. If you first learn how to solve simple equations, then two-step equations and build on that, you will be solving multi-step equations with ease.

Algebraic equations in the simplest form are linear equations. You need to solve for the variable in the equation. To do so, you must isolate the variable on one side of the equals sign and the numbers on the other side. The number in front of the variable (which it is multiplied by, the "coefficient") needs to be equal to one and then you solve the equation for the variable. Whatever math operation you do on one side of the equals sign must also be done on the other side to arrive at a variable with a one in front of it. Make sure and follow the order of operations by multiplying and dividing first, then doing the addition and subtraction. Here is an example of a simple algebraic equation:

\(x – 6 = 10\)

Add 6 to each side of the equation to isolate the variable ​x​.

\(x – 6 + 6 = 10 + 6\)
\(x = 16\)

Addition and subtraction equations are solved by isolating the variable on one side by adding or subtracting the same amount to each side of the equals sign. For example:

\(n – 11 = 14 + 2\)
\(n – 11 + 11 = 16 + 11\)
\(n = 27\)

You solve a two-step equation just as you do a single step equation such as the above example. The only difference is that it takes an additional step to solve, thus the two-step equation. You isolate the variable and then divide to make its coefficient equal to one. For example:

\(3x + 4 = 15 \
\,\
3x + 4 – 4 = 15 – 4 \
\,\)
\(3x = 11 \
\,\)
\(\frac{3x}{3} = \frac{11}{3} \
\,\)
\(x = \frac{11}{3}\)

In the above example, the variable was isolated on one side of the equals sign in the first step and then division was necessary as a second step because the variable had a coefficient of 3.

Multi-step equations have variables on both sides of the equals sign. You solve them in the same manner as the other equations by getting the variable isolated and solving for the answer. After you isolate the variable on one side you get a new equation to solve. For example:

\(4x + 9 = 2x – 6\)
\(4x – 2x + 9 = 2x – 2x – 6\)
\(2x + 9 = -6\)

Solve the new equation.

\(2x + 9 – 9 = – 6 – 9\)
\(\,\)
\(2x = -15\)
\(\,\)
\(\frac{2x}{2} = \frac{-15}{2}\)
\(\,\)
\(x = \frac{-15}{2}\)

For another example, watch the video below: