Solve and graph the solution set on a number line. x + 3X - 2+ 134Al

Given information is: x+34≥x-23+1 Solve and graph the solution set on a number line.

Answered: x + 3 X - 2 + 1 3 4 Al

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.7: Rational Expressions

Problem 8E

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Question

Solve and graph the solution set on a number line.

Expert Solution

Step 1

Given information is:

$\frac{x + 3}{4} \geq \frac{x - 2}{3} + 1$

Solve and graph the solution set on a number line.

Step 2

The solution of the given inequality,

$\begin{array}{rcl} \frac{x + 3}{4} & \geq & \frac{x - 2}{3} + 1 \\ \frac{x + 3}{4} \cdot 12 & \geq & \frac{x - 2}{3} \cdot 12 + 1 \cdot 12 \\ 3 (x + 3) & \geq & 4 (x - 2) + 12 \\ 3 x + 9 & \geq & 4 x + 4 \\ 3 x + 9 - 9 & \geq & 4 x + 4 - 9 \\ 3 x & \geq & 4 x - 5 \\ 3 x - 4 x & \geq & 4 x - 5 - 4 x \\ - x & \geq & - 5 \\ |x| & \leq & 5 \end{array}$

Hence, the solution is $|x| \leq 5$ .

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