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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 for \(x\) are -4 and -3.

Step by step solution

01

Isolate the absolute value

Subtract 2 from both sides of the equation: \(|2x-3| > 7- 2\) which simplifies to \(|2x-3| > 5\)
02

Deal with the absolute value

Set up two equations, one for \(2x-3 > 5\) and one for \(2x-3 < -5\) based on the absolute value definition.
03

Solve the two equations

For \(2x-3 > 5\), add 3 to both sides and divide by 2, resulting in \(x > 4\). For \(2x - 3 < -5\), add 3 to both sides and divide by 2, resulting in \(x < -1\)
04

Check the solutions against the possible values

The equation is only true for \(x < -1\) or \(x > 4\). Compared to the given possibilities, the only solutions are therefore options a and b as only these fall into the result range we found.

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