SAT Math skill page

SAT Inequalities Practice

Turn inequality words like at least, at most, greater than, and no more than into clean SAT Math setups.

Practice inequalities in Dolphin SAT Practice questions

10-16 min practice time3 questions on pageHeart of Algebra

Practice time10-16 min

Question bank3 questions

Best forHeart of Algebra

What this tests

What to know for this SAT skill

Solve one-variable inequalities
Flip the inequality sign when multiplying or dividing by a negative
Translate at least and at most into symbols
Interpret solution ranges in context

Dolphin question bank

Practice your skill

Question 1 of 3Easy

Normal body temperature for an adult is

b e tw ee n 97. 8^{\circ} F

and

9 9^{\circ} F

, inclusive. If Kevin, an adult male, has a body temperature that is considered to be normal, which of the following could be his body temperature?

$96. 7^{\circ} F$
$97. 6^{\circ} F$
$97. 9^{\circ} F$
$99. 7^{\circ} F$

Show answer and solution

Correct answer $C .97. 9^{\circ} F$

Solution walkthrough

Normal body temperature must be greater than or equal to $97. 8^{\circ} F$ but less than or equal to $9 9^{\circ} F$ .
Of the given choices, $97. 9^{\circ} F$ is the only temperature that fits these restrictions.

Why the other choices miss

Choices A and B are incorrect. These temperatures are less than

97. 8^{\circ} F

, so they don’t fit the given restrictions. Choice D is incorrect. This temperature is greater than

9 9^{\circ} F

, so it doesn’t fit the given restrictions.

Question 2 of 3Hard

Which of the following points is a solution to the inequality 3x + 4y < 12?

(0, 3)
(2, 1)
(4, 0)
(3, 2)

Show answer and solution

Correct answerB. (2, 1)

Solution walkthrough

To determine which point is a solution to the inequality $3 x + 4 y < 12$ , substitute the coordinates of each point into the inequality and check if the inequality holds true.

Question 3 of 3Easy

During spring migration, a dragonfly traveled a minimum of 1,510 miles and a maximum of 4,130 miles between stopover locations. Which inequality represents this situation, where d is a possible distance, in miles, this dragonfly traveled between stopover locations during spring migration?

$d \leq 1, 510$
$1, 510 \leq d \leq 4, 130$
$d \geq 4, 130$
$4, 130 \leq d \leq 5, 640$

Show answer and solution

Correct answer $B .1, 510 \leq d \leq 4, 130$

Solution walkthrough

It's given that during spring migration, a dragonfly traveled a minimum of 1,510 miles and a maximum of 4,130 miles between stopover locations.
It's also given that $d$ represents a possible distance, in miles, this dragonfly traveled between stopover locations.
It follows that the inequality $1, 510 \leq d \leq 4, 130$ represents this situation.

Why the other choices miss

Choice A is incorrect. This inequality represents a situation in which a dragonfly traveled a maximum of 1,510 miles between stopover locations. Choice C is incorrect. This inequality represents a situation in which a dragonfly traveled a minimum of 4,130 miles between stopover locations. Choice D is incorrect. This inequality represents a situation in which a dragonfly traveled a minimum of 4,130 miles and a maximum of 5,640 miles between stopover locations.

Avoid these traps

Common mistakes on this skill

Forgetting to reverse the inequality

Multiplying or dividing both sides by a negative number reverses the inequality symbol.

Ignoring whether the endpoint is included

A strict inequality excludes the boundary value, while <= or >= includes it.

Study plan

How to practice this skill in Dolphin

Solve the inequality while recording any step that uses a negative multiplier or divisor.
Test one value from the proposed solution region in the original inequality.
Match the symbol to the correct endpoint and shading on a graph.

Practice inequalities in Dolphin SAT

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Skill cluster

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FAQ

Questions about SAT Inequalities Practice

When does an inequality sign reverse?

It reverses only when both sides are multiplied or divided by a negative quantity.

How can I check an inequality solution?

Substitute one value inside the solution region and one outside it into the original inequality.