Solving Linear Equations Step by Step
The golden rule of equations: whatever you do to one side, do to the other. Here is a repeatable process you can trust every time.
A linear equation is any equation where the variable appears to the first power — no squares, no square roots, just x by itself. Solving one means isolating the variable on one side of the equals sign.
The balance scale idea
Think of the equals sign as the center of a balance scale. Both sides weigh the same. As long as you do the exact same operation to both sides, the scale stays balanced and the equation stays true.
A reliable step-by-step process
- 1Subtract 3 from both sides to undo the addition: 2x = 8.
- 2Divide both sides by 2 to undo the multiplication: x = 4.
- 3Check by substituting back: 2(4) + 3 = 11. It works!
When the variable is on both sides
Sometimes x shows up on the left and the right. Gather the variable terms on one side first, then solve as usual.
- 1Subtract 3x from both sides: 2x - 2 = 8.
- 2Add 2 to both sides: 2x = 10.
- 3Divide by 2: x = 5.
Always finish by checking your answer. Substituting the value back into the original equation is the single best habit you can build in algebra.
Written by Mathew Joane
Algebra teacher on a mission to make math feel less like memorizing and more like understanding.