Solve the following inequalities: (a) 3+x>7 (b) 3 t<6 (c) z-2 ≥5 (d) (p)/(3) ≤2

Name: Problem 1, Chapter 5: Higher Engineering Mathematics
Uploaded: 2021-12-29T18:18:14-08:00
Duration: 3 min 26 s
Channel: Mirza Aslam Beig
Description: Solve the following inequalities: (a) 3+x>7 (b) 3 t<6 (c) z-2 ≥5 (d) (p)/(3) ≤2

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Solve the following inequalities: (a) 3+x>7 (b) 3 t<6 (c)...

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Key Concepts

Linear Inequalities

Linear inequalities involve expressions where variables are to the first power and are related by inequality symbols (such as >, <, ?, ?) rather than equality. They describe a range of possible solutions on a number line, and solving them typically involves similar methods to solving linear equations, with additional considerations for the direction of the inequality.

Isolating the Variable

One of the key techniques in solving inequalities is isolating the variable on one side of the inequality sign. This process involves applying inverse operations—such as addition, subtraction, multiplication, and division—to both sides in order to keep the inequality balanced, thereby determining the set of values that satisfy the inequality.

Properties of Inequality Operations

When working with inequalities, the properties of operations play an essential role. For most operations, such as adding or subtracting the same quantity from both sides, the direction of the inequality remains unchanged. However, special care must be taken when multiplying or dividing both sides by a negative number, as this operation requires reversing the inequality sign. This fundamental property ensures the solution set accurately reflects the underlying relationship described by the inequality.

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