SAT Math · Heart of Algebra
Linear equations in one variable
Solving ax + b = c style equations and isolating a variable.
What's tested in this subtopic
These items present a linear equation in a single variable and ask you to solve for that variable. The variable may appear on both sides; the equation may include nested parentheses, fractional coefficients, or a variable in a denominator that turns out to cancel cleanly. The test occasionally hides a one-step equation inside a sentence-long word problem, where two-thirds of the difficulty is parsing the English.
Tactics that actually move your score
Get the variable on one side using inverse operations and combine like terms before you solve. Watch for fractional coefficients — multiplying both sides by the LCD eliminates fractions and reduces arithmetic errors. When a variable appears in a denominator, note the restricted value (the denominator can't equal zero) and check at the end that your answer doesn't violate it. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy If 7x − 2 = 26, what is the value of x?
- Easy If 5x + 9 = 54, what is the value of x?
- Medium If 5x + 10 = 55, what is the value of x?
- Medium If 5x + 12 = -38, what is the value of x?
- Medium If 6x + 1 = 25, what is the value of x?
- Hard If 5x + 10 = 35, what is the value of x?
- Easy If 3x + 8 = -19, what is the value of x?
- Easy If 2x − 1 = 11, what is the value of x?
- Medium If 4x − 10 = 26, what is the value of x?
- Medium If 7x + 8 = -34, what is the value of x?
- Medium If 2x + 10 = 2, what is the value of x?
- Hard If 6x + 1 = 7, what is the value of x?
- Easy If 3x − 8 = 4, what is the value of x?
- Easy If 4x + 0 = -40, what is the value of x?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.