Linear equations in one variable are the most common math you'll see on this test — and the foundation for almost everything else. Master the 'undo' process and you'll bank points fast.
Collecting variable terms when x appears on both sides.
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Quick check
Check your understanding with a question from this topic:
Pens cost 4each.Howmanypenscanbepurchasedwith48?
Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).
Worked examples
Example 1
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Example 2
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Example 3
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Common pitfalls
Only changing one side of the equation
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Forgetting to distribute to every term
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Dividing too early
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Sign errors when moving terms
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Key takeaways
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Watch & learn
Curated Khan Academy walkthroughs on Linear Equations in 1 Variable. They're complementary to this lesson — watch one if a written explanation isn't clicking, or after to reinforce.
Tracks your progress across lessons.
Try it yourself
5 practice questions on Linear Equations in 1 Variable, drawn from the question bank. The tutor is one click away if you get stuck.
A linear equation in one variable is an equation where you're solving for a single unknown (usually x), and that variable is never raised to a power, never multiplied by another variable, and never stuck inside a square root. It's just x to the first power. Examples: 3x + 11 = 32 or 5(x - 2) = 20.
Your goal is always the same: get the variable by itself on one side of the equals sign. The number you end up with is the solution — the value that makes the equation true.
The golden rule: whatever you do to one side, you must do to the other. The equals sign means both sides are balanced, like a scale. If you add 4 to the left, add 4 to the right. If you divide the left by 3, divide the right by 3.
To isolate x, you undo operations in reverse order. Think about what's been done to x:
First undo addition or subtraction (the terms being added or removed).
Then undo multiplication or division (the coefficient stuck to x).
Here's the pattern with 3x + 11 = 32:
Subtract 11 from both sides: 3x = 21
Divide both sides by 3: x = 7
That's it. Two moves.
If the equation has parentheses, distribute first: 5(x - 2) = 20 becomes 5x - 10 = 20. If the variable appears on both sides, move all the x terms to one side and all the plain numbers to the other:
Word problems are linear equations in disguise. "Pens cost 4each;howmanycanyoubuywith48?" is just 4x = 48, so x = 12. The skill is translating the sentence into an equation, then solving normally.
Always check by plugging your answer back in. If x = 7 in 3x + 11, you get 21 + 11 = 32. âś“ That match confirms you're right.
Solve for x: 5x - 9 = 26
If 4(x + 3) = 2x + 22, what is the value of x?
A taxi charges a flat fee of 3plus2 for every mile driven. If a ride costs $19, how many miles was the ride?
If you subtract a number from the left, you MUST subtract it from the right too. Forgetting to balance both sides is the single most common error — treat the equals sign like a scale that must stay level.
In 5(x - 2), students multiply the 5 by x but forget the -2, writing 5x - 2 instead of 5x - 10. Distribute to everything inside the parentheses.
In 3x + 11 = 32, don't divide by 3 before subtracting 11 — you'd have to divide every term. Clear the added/subtracted number first, then divide by the coefficient.
Moving a term across the equals sign flips its sign. Better yet, don't 'move' — actually add or subtract from both sides so you never lose track of a negative.
Goal: isolate the variable using inverse operations on both sides.
Undo addition/subtraction first, then multiplication/division.
Distribute through parentheses before collecting terms.
Put all variable terms on one side, all constants on the other.
Always plug your answer back in to confirm it works.
Linear Equations in 1 Variable — Learn | UnlimitedTests