GMAT Exam > GMAT Notes > Quantitative for GMAT > Solved Examples - Beyond Equations: Inequalities & Absolute Value
Solved Examples - Beyond Equations: Inequalities & Absolute Value | Quantitative for GMAT PDF Download
Section - 1
Draw the following inequalities on the number line provided:
Ques 1: 
Ans:
Ques 2: 
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Ques 3: 
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Ques 4: 
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Ques 5: 
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Section - 2
Ques 6: a is less than b.
Ans: a is less than b.
a < b
Ques 7: Five times x is greater than 10.
Ans: Five times x is greater than 10.
5x > 10
Ques 8: Six is less than or equal to 4x.
Ans: Six is less than or equal to 4x.
6 < 4x
Ques 9: The price of an apple is greater than the price of an orange.
Ans: The price of an apple is greater than the price of an orange.
Let a = the price of an apple
Let o = the price of an orange
a > o
Note: In this problem, we set up our variables to refer to prices— not the number of apples and oranges.
Ques 10: The total number of members is at least 19.
Ans: The total number of members is at least 19.
Let m — the number of members
m > 19
Section - 3
Solve the following inequalities.
Ques 11: x + 3 ≤- 2
Ans:
Ques 12: f - 4 ≤ 13
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Ques 13: 3b≥ 12
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Ques 14: -5x > 25
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Ques 15: -8<-4y
Ans:
Section - 4
Solve the following equations.
Ques 16: 2z + 4 ≥-18
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Ques 17: 7y - 3 ≤ 4y + 9
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Ques 18: b/5 ≤ 4
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Ques 19: d + 3/2<8
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Ques 20: 4x/ 7 ≤ 15 + x
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Section - 5
Solve the following inequalities.
Ques 21: 3 ( x - 7 ) ≥ 9
Ans:
Ques 22: 
Ans:
Ques 23: 2x - 1.5 > 7
Ans: 
Ques 24: 
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Ques 25: 
Ans:
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FAQs on Solved Examples - Beyond Equations: Inequalities & Absolute Value - Quantitative for GMAT
| 1. What is an inequality? |  |
Ans. An inequality is a mathematical statement that compares two quantities and expresses that one quantity is greater than, less than, or not equal to the other quantity. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to) to represent the relationship between the two quantities.
| 2. How do you solve an inequality? | |
Ans. To solve an inequality, you follow similar principles as solving equations. However, there are some differences depending on the type of inequality. For example, if there is a variable on both sides of the inequality, you need to isolate the variable on one side. When multiplying or dividing both sides by a negative number, you also need to reverse the inequality sign. It's important to carefully apply the rules and solve for the variable to find the range of values that satisfy the inequality.
| 3. What is absolute value? | |
Ans. Absolute value is a measure of the distance between a number and zero on a number line. It is always positive or zero. The absolute value of a number is represented by two vertical bars surrounding the number. For example, the absolute value of -5 is written as |-5|, which equals 5. The absolute value of a positive number is the number itself, while the absolute value of a negative number is the opposite of that number.
| 4. How do you solve absolute value inequalities? | |
Ans. To solve absolute value inequalities, you need to consider two cases. First, if the absolute value expression is greater than a positive number, you can remove the absolute value bars and write two separate inequalities, one without the absolute value and one with the opposite sign. Solve both inequalities separately to find the range of values that satisfy the inequality. Second, if the absolute value expression is less than a positive number, you can remove the absolute value bars and write a single inequality. Solve it to find the range of values that satisfy the inequality.
| 5. What are some real-life applications of inequalities and absolute value? | |
Ans. Inequalities and absolute value have numerous real-life applications. For instance, they are used in financial planning to determine spending limits or investment returns. In physics, inequalities are used to analyze motion and determine the range of possible values for variables. In computer science, inequalities are used in algorithms and optimization problems. Absolute value is often used in distance calculations, error analysis, or determining the magnitude of a vector. These concepts play a crucial role in various fields where comparing quantities or measuring distances is important.
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