Study Guide

Linear Equations in One Variable

Linear equations in one variable involve finding the value of a single unknown. These are foundational SAT math problems, often embedded in word problem contexts.

Key Rules

To solve: isolate the variable by performing the same operation on both sides.
Distribution first: expand parentheses before combining like terms.
When there are fractions, multiply both sides by the LCD to clear them.
Special cases: if the variable cancels and you get a true statement (0=0), there are infinite solutions. If false (3=7), there are no solutions.

Common Mistakes to Avoid

Sign errors when moving terms across the equals sign.
Forgetting to distribute a negative sign across all terms in parentheses.
Not multiplying ALL terms by the LCD when clearing fractions.
Confusing "no solution" with "solution is 0."

SAT Strategy Tips

→For word problems: identify what the variable represents, then translate each piece of the problem into an equation.
→Always check your answer by substituting back into the original equation.
→If the answer choices are numbers, plug them in rather than solving algebraically.
→Watch for "twice as many," "three less than," and similar language — translate carefully.

Example Question

If 3x + 7 = 22, what is the value of x?

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Linear Equations in One Variable

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