Algebra • 35% of test
Linear Equations
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Linear Equations?
Linear equations are the foundation of SAT Math, appearing more than any other topic. These one-variable equations test your ability to isolate variables, distribute, combine like terms, and solve for unknowns in real-world contexts.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
What steps solve any linear equation?
1) Distribute, 2) Combine like terms, 3) Move variables to one side, 4) Move constants to other side, 5) Divide by coefficient.
How do I check my answer?
Substitute your solution back into the original equation. Both sides should be equal.
What if there's no solution?
If you get a false statement like 5 = 3, the equation has no solution. If you get a true statement like 0 = 0, infinitely many solutions exist.
How do I handle fractions?
Multiply both sides by the LCD to eliminate fractions first, then solve normally.
What are common word problem keywords?
'Is' means =, 'more than' means +, 'less than' means −, 'of' often means ×, 'per' often means ÷.
How many linear equation questions appear?
Typically 4-6 questions, making this the most common single topic. Mastering it is essential for a high score in the <a href='/math'>SAT Math section</a>.
Can I solve linear equations with variables on both sides?
Yes, move all x terms to one side first by adding or subtracting them from both sides, then isolate as usual.
What is the difference between an expression and an equation?
An equation contains an equals sign (=) showing that two expressions are equal; an expression is just a combination of numbers and variables.
How do I solve for a variable in terms of other variables (Literal Equations)?
Isolate the target variable just like you would with numbers. For example, in A = Lw, to solve for L, divide both sides by w.
Is there a trick for equations with many decimals?
Yes, multiply every term in the equation by 10, 100, or 1000 to eliminate the decimals before solving.
What if the result is 0 = 0?
This means the equation is an identity and has infinitely many solutions; any value for the variable will work.
What if the result is 0 = 5?
This is a contradiction, meaning there is no value that makes the equation true, so there is no solution.
How do I handle negative signs in front of parentheses?
Distribute the negative to every term inside. For example, -(x - 4) becomes -x + 4.
Does the order of operations matter when solving?
Yes, you generally perform PEMDAS in reverse order (SADMEP) to unwrap the variable from its operations.
What is the most common mistake in linear equations?
Sign errors, especially when subtracting terms or distributing negatives. Practice these fundamentals with our <a href='/math/linear-equations/beginner'>Beginner Linear Equations sets</a>.