Solving equations of the form ax + b = c, including equations with variables on both sides, fractions, and no-solution or infinite-solution cases.
47
Total questions
22
Easy
14
Medium
11
Hard
These are the most direct algebra questions on the SAT: solve for x in a single equation. The test raises the difficulty with fractions, decimals, variables on both sides, and special cases — equations engineered to have no solution (the variable terms cancel and leave a false statement) or infinitely many solutions (both sides are identical).
Work these mechanically: clear fractions by multiplying through by the common denominator first, then collect variable terms on one side. For no-solution/infinite-solution questions, don't solve — compare coefficients. If the x-coefficients match but constants differ, there's no solution; if everything matches, every x works.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: B
Choice B is correct. Dividing each side of the given equation by 9 yields w = 7. Therefore, w/3 = 7/3.
Choice A is incorrect and may result from inverting the fraction.
Choice C is incorrect. This is the value of w, not w/3.
Choice D is incorrect. This is the value of 3w, not w/3.
Correct answer: B
Choice B is correct. The volume of the tank at a given time is equal to its volume when the hose was connected plus the number of gallons added. In the given equation, 31 represents the volume of the tank at the given time, and 10 represents the volume of the tank when the hose was first connected. It follows that 3t represents the number of gallons added from the time the hose was connected until the tank reached 31 gallons. Since t represents the number of minutes, 3 must represent the average number of gallons added per minute.
Choice A is incorrect and may result from interpreting the coefficient 3 as tripling instead of as increasing by 3 each minute.
Choice C is incorrect. The volume of the tank when 1 minute had passed was 3(1) + 10 = 13 gallons, not 3 gallons.
Choice D is incorrect. No information is given to connect the filling of one particular tank to similar tanks.
Linear Equations in Two Variables
Working with equations like y = mx + b: interpreting slope and intercepts, converting between forms, and connecting equations to their graphs.
Linear Functions
Modeling real situations with linear functions — constant rates of change, initial values, and evaluating or interpreting f(x) in context.
Linear Inequalities
Solving and interpreting inequalities in one or two variables, including flipping the inequality sign and identifying solution regions.
Systems of Linear Equations
Solving pairs of linear equations by substitution or elimination, and reasoning about when systems have one, none, or infinitely many solutions.
47 Linear Equations in One Variable questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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