Grade 6 Math Practice Test: Writing and Graphing Inequalities
- Writing and Graphing Inequalities
- 10 questions
- 12 minutes
This test practices inequalities such as x > c and x ≤ c: writing them from words, reading their graphs and checking solutions. Tip: an open circle means the number itself is not included, a closed circle means it is.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
An elevator can safely carry no more than 1,500 pounds. Which inequality shows the weights w, in pounds, it can safely carry?
Correct answer: A
"No more than 1,500" means 1,500 or less, so 1,500 itself is allowed: w ≤ 1,500. w < 1,500 leaves out exactly 1,500 pounds.
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Question 2
Which inequality is shown on the number line?
Correct answer: C
The shading goes to the right, toward greater numbers, and the circle at 4 is open, so 4 is not included: x > 4. A closed circle would show x ≥ 4.
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Question 3
Which inequality is shown on the number line?
Correct answer: D
The shading goes to the left, toward smaller numbers, and the circle at −2 is filled in, so −2 is included: x ≤ −2.
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Question 4
Which number is a solution of the inequality x > 7.5?
Correct answer: B
8 is greater than 7.5. 7.5 is not a solution because x must be greater than 7.5, not equal to it.
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Question 5
Which set contains only solutions of y ≤ 3?
Correct answer: C
Every number in the set must be 3 or less. 0, 2 and 3 all are; the set 2, 3 and 4 fails because 4 is greater than 3.
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Question 6
Which phrase means the same as x < 6?
Correct answer: C
The symbol < is read "is less than." "At most 6" includes 6 itself and would be written x ≤ 6.
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Question 7
A town issues a cold-weather warning whenever the temperature is below −3°F. Which inequality shows temperatures t, in °F, that are below −3°F?
Correct answer: A
"Below −3" means less than −3, and −3 itself is not below −3, so t < −3. t > −3 would mean warmer temperatures.
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Question 8
How many positive whole numbers are solutions of x ≤ 5?
Correct answer: B
The positive whole numbers that are 5 or less are 1, 2, 3, 4 and 5, which is 5 numbers. Choosing 4 forgets that 5 itself is included.
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Question 9
How many numbers are solutions of the inequality x > 9?
Correct answer: A
Every number greater than 9, such as 9.5, 10 or 1,000, is a solution, so there are infinitely many. The equation x = 9 has exactly one solution, but the inequality does not.
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Question 10
Jo has $25 to spend at a fair. She does not have to spend all of it. Which inequality shows the amounts a, in dollars, that she can spend?
Correct answer: D
She can spend any amount up to and including $25, so a ≤ 25. a < 25 would wrongly say she cannot spend exactly $25.
Questions you leave blank are not counted as wrong.
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