Algebra

Absolute Value

Absolute Value Inequalities

         

Which of the following represents the correct value of x x if 8x+b>c, \lvert 8x \rvert + b > c, and c>b c>b?

Solve for x x :

x22x3<3x1. x^2 - 2x -3 < 3 |x-1|.

If the solution set of the system of inequalities: {a+1<2b1<12\begin{cases}\lvert a+1 \rvert < 2\\ \lvert b-1 \rvert <12 \end{cases} is x<a+b<y, x < a+b < y, what are xx and y?y?

For all non-zero real numbers (x,y) (x, y) , which of the following is larger:

A=x1+x+y1+y or B=x+y1+x+y? A = \frac{ |x| } { 1 + |x| } + \frac{ |y| } { 1 + |y| } \text{ or } B = \frac{ |x+y| } { 1 + |x+y| } ?

The inequality 2x+8+16<32 \lvert 2x+8 \rvert + 16 < 32 implies that a<x<b a < x < b . What is ba b-a?

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