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Chapter 2: Problem 45

Solve the inequality. Then graph the solution set. $$\frac{2}{x+5}>\frac{1}{x-3}$$

Short Answer

Expert verified
The solution to the inequality is \(x > 11\), but \(x \neq -5, 3\) due to the original division by zero.

Step by step solution

01

Clear fractions

To avoid dealing with fractions, clear the fractions by multiplying each side of the inequality by \((x+5)(x-3)\), then simplify the result.\[2(x-3) > (x+5)\]
02

Expand and Simplify

Expand and simplify the inequality. Obtain a normal form of inequality by moving all terms to one side and making the other side equals zero.\[2x - 6 > x + 5\] becomes \[x > 11\] after simplification.
03

Checking the division by zero point

It is noted that \(x\neq-5,3\) because these values will result in division by zero in the original inequality.
04

Graph the solution

Draw a number line, put 11, -5 and 3 on the line. Since we are looking for \(x > 11\), we will make an open circle at 11 and draw an arrow to the right. Do not mark -5 and 3 on the line because these points are not part of the solution set.

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