express the set of numbers x satisfying the given condition as an interval. |4 x-1| ≤8

Name: Problem 17, Chapter 1: Calculus for AP
Uploaded: 2019-05-15T03:59:57-08:00
Duration: 2 min 42 s
Channel: Dishary Hossain
Description: express the set of numbers x satisfying the given condition as an interval. |4 x-1| ≤8

step 1 Hi, so today we will be solving this question, express the set of numbers x, satisfying the give

Express the set of numbers x satisfying the given condition...

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Key Concepts

Interval Notation

Interval notation is a concise way to express a set of numbers lying between two endpoints. It uses brackets to indicate that an endpoint is included (closed interval) and parentheses to indicate that it is excluded (open interval), thereby providing a clear representation of all values that satisfy a given inequality.

Algebraic Manipulation of Inequalities

This concept refers to the methods used to simplify and solve inequalities, such as isolating the variable by performing identical operations on all parts of the inequality. The techniques are similar to those used in solving equations but require careful attention to the direction of the inequality, especially when multiplying or dividing by negative numbers.

Absolute Value Inequality

An absolute value inequality involves an expression inside the absolute value sign being constrained by a non-negative number. It is often interpreted by rewriting the inequality as a compound inequality, stating that the expression is between the negative and positive of the given constant.

Compound Inequality

A compound inequality represents two simultaneous inequalities that together specify a range of values. In the context of absolute value inequalities, it is used to describe the condition where the expression must lie between two bounds.

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