Inequalities Quiz: Greater Than And Less Than Basics
Test your knowledge of inequalities with our "Greater Than and Less Than Basics Quiz." What do you know about Inequalities: Greater than and less than basics? In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality). Whether you're a budding mathematician or simply intrigued by the fundamental principles that govern numerical relationships, this quiz is your gateway to mastering the basics of inequalities.
Sharpen your understanding of mathematical comparisons, where the symbols of greater than (>) and less than (<) take center stage. This quiz is designed to unravel the Read moreintricacies of non-strict inequalities, exploring the diverse ways in which numbers relate to each other without the strict constraints of inequality.
Inequalities: Greater Than and Less Than Basics Questions and Answers
- 1.
If x>5 and x<10, which of the following could be a value of x?
- A.
4
- B.
11
- C.
6
- D.
10
Correct Answer
C. 6Explanation
Given the inequality x>5x > 5 and x < 10x<10, the value of xxx must be greater than 5 and less than 10.
4 is not greater than 5, so it doesn't satisfy x>5.
11 is not less than 10, so it doesn't satisfy x<10x < 10.
10 is not less than 10, so it doesn't satisfy x<10x < 10.
6 is greater than 5 and less than 10, so it satisfies both conditions x>5x > 5 and
x < 10x<10.
Therefore, the value of x could be 6.Rate this question:
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- 2.
Solve the inequality: 3y−7<5. What is the range of y?
- A.
Y<4
- B.
Y<2
- C.
Y>4
- D.
Y>2
Correct Answer
A. Y<4Explanation
To solve 3y−7<5:
Add 7 to both sides: 3y−7+7<5+7
3y<12
Divide both sides by 3:
3y/3 < 12/3
y<4Rate this question:
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- 3.
Which of the following inequalities represents "7 is greater than 3"?
- A.
7<3
- B.
7>3
- C.
3>7
- D.
3=7
Correct Answer
B. 7>3Explanation
The inequality 7>3 correctly states that 7 is greater than 3. In mathematical terms, the symbol ">" denotes that the number on the left is greater than the number on the right. Hence, 7>3 is the correct representation of the statement "7 is greater than 3".Rate this question:
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- 4.
Which inequality symbol correctly completes the statement: −2 _−5?
- A.
>
- B.
<
- C.
≥
- D.
≤
Correct Answer
A. >Explanation
Negative numbers can be tricky. On a number line, numbers to the right are greater than those to the left. Therefore, −2 is greater than −5 because it is closer to zero. The correct inequality symbol to complete the statement is >, making it −2>−5.Rate this question:
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- 5.
For which values of x is the inequality x2<16 true?
- A.
−4<x<4
- B.
X>4
- C.
X<−4
- D.
X≤4
Correct Answer
A. −4<x<4Explanation
The inequality x2<16 means that the square of xxx must be less than 16. Taking the square root of both sides of the inequality x2<16, we get: ∣x∣<4 This implies that x is between -4 and 4, but does not include -4 and 4 themselves (since x2 would be 16 if x were ±4). Therefore, the values of x that satisfy x2<16 are −4<x<4.Rate this question:
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- 6.
Solve the inequality: 2(x−3)>4. What is the range of x?
- A.
X>5
- B.
X>4
- C.
X>3
- D.
X>2
Correct Answer
A. X>5Explanation
To solve the inequality 2(x−3)>4:
First, divide both sides by 2: 2(x-3)/2> 4/2= x−3>2
Next, add 3 to both sides to isolate x: 3+(x-3)>2+3= x>5
Therefore, the range of x that satisfies the inequality 2(x−3)>4 is x>5.Rate this question:
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- 7.
If a<b and b<c, which of the following is true?
- A.
A>c
- B.
A<c
- C.
C<a
- D.
C=a
Correct Answer
B. A<cExplanation
If a is less than b and b is less than c, then by the transitive property of inequalities, a must be less than c. This is because aaa being less than b and b being less than c logically means that aaa is also less than c.Rate this question:
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- 8.
Which value of x satisfies both inequalities: x+2>5 and x−3<1?
- A.
X>3
- B.
X<4
- C.
3<x<4
- D.
2<x<3
Correct Answer
C. 3<x<4Explanation
Solve each inequality separately:
For x+2>5: Subtract 2 from both sides: x+2-2 > 5-2= x>3
For x−3<1: Add 3 to both sides: x-3+3<1+3 = x<4
Combining these results, the values of x that satisfy both inequalities are those that lie between 3 and 4: 3<x<4Rate this question:
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- 9.
Which of the following is true if 5x+3≤18?
- A.
X≥3
- B.
X≤3
- C.
X≥5
- D.
X≤5
Correct Answer
B. X≤3Explanation
To solve the inequality 5x+3≤18:
Subtract 3 from both sides: 5x+3−3 ≤ 18−3 = 5x ≤ 15
Next, divide both sides by 5: 5x/5 ≤ 15/5 = x ≤ 3
Therefore, x ≤ 3 is the correct solution.Rate this question:
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- 10.
Solve the compound inequality: 1<2y+3<7. What is the range of y?
- A.
−1<y<2
- B.
0<y<2
- C.
1<y<3
- D.
−2<y<1
Correct Answer
A. −1<y<2Explanation
Solve the compound inequality in two parts:
Solve 1<2y+3:
Subtract 3 from both sides: 1−3 < 2y+3 - 3 = -2 < 2y
Divide by 2: -2/2 < 2y/2 = -1 < y
Solve 2y+3<7:
Subtract 3 from both sides: 2y+3 -3 < 7-3 = 2y < 4
Divide by 2: 2y/2 < 4/2 = y< 2
Combining these results, we get: −1 < y < 2
Rate this question:
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Current Version
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Jun 24, 2024Quiz Edited by
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Jan 20, 2018Quiz Created by
Livyn
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