   Chapter 1, Problem 4RE

Chapter
Section
Textbook Problem

In Exercises 1–4, find the values of x that satisfy the inequality (inequalities).4. 2x2 > 50

To determine
The value of x that satisfies the inequality 2x2>50 .

Explanation

Given:

The given inequality is x3>2orx+3<1 .

Formula used:

Formula to calculate the difference of square is

A2B2=(A+B)(AB)

Calculation

Simplify the inequality.

2x2>50

Multiply both sides of the above inequality by 12

2x250>50502x250>02(x225)>02(x252)>0 (1)

Formula to calculate the difference of square is

A2B2=(A+B)(AB)

Substitute x for A and 5 for B in above equation

x252=(x+5)(x5)

Substitute (x+5)(x5) for (x252) in equation (1).

2(x+5)(x5)>0

The above inequality holds if and only if (x+5)>0 and (x5)>0 or (x+5)<0 and (x5)<0 .

Case 1: (x+5)>0and(x5)>0

Simplify the first inequality

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