Concept Overview
A linear equation is an equation where the variable has power 1.
Solving an equation means finding the value of the variable that makes the statement true.
Solving Linear Equations explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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A linear equation is an equation where the variable has power 1.
Solving an equation means finding the value of the variable that makes the statement true.
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Linear equations are used in ages, prices, distances, patterns, and many word problems.
An equation has an equal sign. Both sides must stay balanced.
To solve an equation, isolate the variable. Isolate means get the variable by itself on one side.
Use inverse operations. Addition and subtraction undo each other. Multiplication and division undo each other.
Whatever operation you do to one side, do the same to the other side.
After solving, substitute the value back into the original equation to check.
Meaning: A linear equation has a variable with power 1.
Definition: A linear equation in one variable can be written in the form a, where a is not 0.
2 is linear because x has power 1.
Meaning: Ontep equations need one inverse operation.
Definition: A ontep equation can be solved in a single operation.
is solved by subtracting 7 from both sides.
Meaning: Twtep equations need two inverse operations.
Definition: A twtep equation has two operations connected to the variable.
3 is solved by subtracting 4, then dividing by 3.
Meaning: The variable may appear on both sides of the equation.
Definition: Collect variable terms on one side and constants on the other side.
For 5, subtract 3x from both sides first.
Easy
Question: Solve .
Medium
Question: Solve 4.
Exam-level
Question: Solve 5.
Doing an operation to only one side
Why it happens: The equation balance idea is missed.
Correct approach: Do the same operation to both sides.
Undoing operations in the wrong order
Why it happens: The expression around x is not read carefully.
Correct approach: For 3, und first, then x3.
Changing signs incorrectly when collecting terms
Why it happens: Moving terms is done mentally.
Correct approach: Write the same operation on both sides instead of skipping steps.
What does solve mean?
It means find the value of the variable that makes the equation true.
Why do we do the same thing to both sides?
Because both sides of an equation must remain equal.
How do I check my answer?
Substitute your value into the original equation and see if both sides match.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.
Meaning: Verification checks whether the answer is correct.
Definition: To verify, substitute the found value into the original equation.
If for , then , so the answer is correct.