One-step linear equations express a value as related to an unknown by a single addition, subtraction, multiplication, or division operation; solving uses the inverse operation while preserving equality, and substitution verifies the resulting solution. The work includes equations with integer or simple rational numbers and connects symbolic equations to balance and algebraic reasoning; it excludes multi-step equations, variables on both sides, and cases involving identities or contradictions.
On this page:
- Learn “Solve one-step linear equations” with a detailed explanation of the concept
- Master “Solve one-step linear equations” with unlimited, free practice problems
- Download (or modify) a free worksheet on Solve one-step linear equations you can use at home or in class with practice problems that scaffold and explore “Solve one-step linear equations” from different perspectives.
- Start working on adaptive units like “Algebra Basic Concepts - Practice” that introduce, teach, or practice “Solve one-step linear equations” to maximize your learning.
Detailed Explanation: Solve one-step linear equations
A one-step equation can be solved by using the inverse operation to isolate the variable. Whatever you do to one side, do to the other side to keep the equation balanced.
Solve:
The equation subtracts from . The inverse of subtraction is addition, so add to both sides:
Simplify:
Check the solution by substituting for in the original equation:
Since the statement is true, the solution is .
Learn by doing: Solve one-step linear equations
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Your results
Practice with unlimited practice problems
Practice:
Linear Equation - One Variable, Two Terms
Earned ?
Download/Modify Free Grade 9 'Solve one-step linear equations' Worksheet
Print this free 'Solve one-step linear equations' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Linear Equation - One Variable, Two Terms
- One-Step Equation - Basic Operations - Solve
- Linear Equation - One Variable, Two Terms, Simple Display
- Linear Equation - Solve for Box, Two Terms, Add and Subtract
- Linear Equation - Solve for Box, Three Terms, Add and Subtract
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Solve one-step linear equations) through scaffolded problems that grow in difficulty as concepts are understood.