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Linear inequalities in one or two variables — SAT practice questions

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Practice 113 Linear inequalities in one or two variables questions in the app

What this topic is

Linear inequalities in one or two variables use symbols such as less than or greater than or equal to in place of an equals sign.

Solving one works like solving an equation, with one exception: multiplying or dividing both sides by a negative number reverses the direction of the inequality. Word problems translate phrases like at most into less than or equal to, and at least into greater than or equal to.

With two variables, a question may list several points and ask which satisfies the inequality, checked by substitution, or show a shaded region on a graph.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

To reserve spots on a bicycle tour, a guide must pay a $43.50 fee plus $14.80 per rider. The guide can spend at most $283. If r is the number of riders, which inequality represents this situation?

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Answer: C — 43.50+14.80r≤283

The reservation cost is 43.50 plus 14.80 for each of r riders. Because the guide can spend at most $283, that cost must satisfy 43.50+14.80r≤283. The first choice reverses the inequality. The second and fourth choices swap the fixed fee with the per-rider charge.

Question 2Easier

Which of the following points is a solution to the inequality 2x−y>5?

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Answer: C — (6,−2)

A point (x,y) is a solution if 2x−y>5. Testing (6,−2): 2(6)−(−2)=14, and 14>5, so this point works. The other three points give 0, 4, and −7, none of which is greater than 5.

Question 3Easier

1<3x−5

Which inequality is equivalent to the given inequality?

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Answer: A — x>2

Adding 5 to both sides gives 6<3x. Dividing both sides by 3 gives 2<x, which is equivalent to x>2.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 113 Linear inequalities in one or two variables questions in the app

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