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Problem Set: Inequalities Video Lecture | Quantitative for GMAT
FAQs on Problem Set: Inequalities Video Lecture - Quantitative for GMAT
| 1. What are inequalities in mathematics? |  |
Ans. Inequalities in mathematics are mathematical expressions that compare two values or quantities, indicating which one is greater than, less than, or equal to the other. They are represented by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Inequalities are used to describe relationships between numbers and are an essential concept in algebra and real analysis.
| 2. How do you solve inequalities with variables? | |
Ans. To solve inequalities with variables, you need to follow similar rules as solving equations. However, there are some additional considerations due to the inequality symbols. The steps generally involve isolating the variable on one side of the inequality sign and determining the appropriate direction of the inequality based on the given conditions. It is important to remember to reverse the inequality sign when multiplying or dividing by a negative number.
| 3. What is the difference between solving an equation and solving an inequality? | |
Ans. The main difference between solving an equation and solving an inequality is the inclusion of the inequality symbols (<, >, ≤, ≥) in the latter. When solving an equation, you are seeking the exact value(s) that satisfy the equation, whereas when solving an inequality, you are determining the range of values that satisfy the given conditions. Inequalities provide a broader range of possible solutions compared to equations.
| 4. How do you graph inequalities on a number line? | |
Ans. Graphing inequalities on a number line is a visual representation of the solution set. To graph an inequality, you first need to identify the appropriate inequality symbol. Then, you mark the corresponding value on the number line and shade the region that satisfies the inequality. If the inequality includes an equal sign (≤ or ≥), you use a solid dot to represent the value on the number line. If the inequality does not include an equal sign (< or >), you use an open dot.
| 5. What are the properties of inequalities? | |
Ans. The properties of inequalities are similar to those of equations. However, there are a few additional properties specific to inequalities. These properties include the addition and subtraction property, the multiplication and division property (with some considerations when multiplying or dividing by negative numbers), and the transitive property. Additionally, when solving a compound inequality, the properties of inequalities can be applied to each individual inequality within the compound inequality.
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