Answered: 1) Solve and check: |x – 1| = 2x + 3.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

1) Solve and check: |x – 1| = 2x + 3.

2) In the NHL, the boards are between 40 and 48 inches tall. Express this as (a) a compound inequality and (b) an absolute value inequality.

3) Solve the system:

2x – y + 3z = 1

x + 2y – z = 4

3x + y + z = 6

Expert Solution

Step 1

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1) Solve and check:

|x – 1| = 2x + 3

Step 2

$| x - 1 | = 2 x + 3$

Case 1:

For $x < 1$

$\begin{array}{l} |x - 1| = 2 x + 3. \\ - (x - 1) = 2 x + 3 (∵ |x| = \{\begin{cases} x x > 0 \\ - x x < 0 \end{cases}) \\ - x + 1 = 2 x + 3 \\ - x - 2 x = 3 - 1 \\ - 3 x = 2 \\ x = \frac{- 2}{3} \end{array}$

Case2:

For $x \geq 1$

$\begin{array}{l} |x - 1| = 2 x + 3. \\ (x - 1) = 2 x + 3 (∵ |x| = \{\begin{cases} x x > 0 \\ - x x < 0 \end{cases}) \\ x - 1 = 2 x + 3 \\ x - 2 x = 3 + 1 \\ - x = 4 \\ x = - 4 \end{array}$

Since we have taken $x \geq 1$ but solution comes $x = - 4 < 1$ ,

so it is not the solution

From case 1 the solution is $x = \frac{- 2}{3}$

From case 2 there is no solution.

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