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Chapter 14: Problem 15

If \(|2 x-3|+2>7,\) which of the following could be the value of \(x ?\) Indicate all such values. a. -4 b. -3 c. -2 d. -1 e. 0 f. 1 g. 2 h. 3

Short Answer

Expert verified
The possible values of \(x\) that satisfy the inequality \(|2 x-3|+2>7\) are a. -4 b. -3, c. -2, and d. -1.

Step by step solution

01

Rewriting the Inequality

The initial absolute value inequality to solve is \(|2 x-3|+2>7\). To isolate the absolute value expression, rewrite the inequality as \(|2 x-3| > 7-2\) which simplifies to \(|2 x-3| > 5\).
02

Breaking Down the Absolute Value Inequality

The inequality \(|2 x-3| > 5\) can be broken down into two separate inequalities. These are \(2 x - 3 > 5\) and \(2 x - 3 < -5\).
03

Solving the First Inequality

Solving \(2 x - 3 > 5\) for \(x\) gives \(x > 4\).
04

Solving the Second Inequality

Solving \(2 x - 3 < -5\) for \(x\) gives \(x < -1\).
05

Testing the Provided Values

The possible values of \(x\) must satisfy one of the inequalities. By testing all the provided values, the set of values that fit the above inequalities are: a. -4 b. -3, c. -2 and d. -1.

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