Select the correct alternative from the given choices. If 6 x+8>7 x-9 and 4 x-7<6 x-3, then the

step 1 So in this question, we are given two inequalities and we are asked to find out what are the val

Select the correct alternative from the given choices. If 6...

Key Concepts

Linear Inequalities

Linear inequalities involve expressions of the first degree and are solved similarly to linear equations, with special consideration for the direction of the inequality sign. When manipulating these inequalities, such as adding, subtracting, multiplying, or dividing by a constant, it is important to remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Compound Inequalities

Compound inequalities consist of two or more inequalities that must be satisfied simultaneously. In problems where multiple inequality conditions are given, each condition is solved independently before combining the solutions to find the set of values that satisfy all conditions concurrently.

Intersection of Inequalities

The intersection of inequalities refers to the common set of values that satisfy all given inequality conditions. This process involves finding the overlap between the solution sets of individual inequalities and results in a final range or interval that represents solutions meeting every condition.

Interval Notation

Interval notation is a standardized way to represent continuous ranges of numbers, where parentheses indicate that endpoints are not included and brackets indicate that endpoints are included. This form of representation is concise and useful for clearly communicating the solution set of inequalities.

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