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Chapter 6: Problem 49

Solve each inequality and graph the solution set on a number line. \(2 x-5<5 x-11\)

Short Answer

Expert verified
The solution to the inequality is \(x > 2\).

Step by step solution

01

Simplify the inequality

The first step is to simplify the given inequality \(2x - 5 < 5x - 11\). This can be achieved by reducing the inequality to a form where all x terms are on one side and the constants are on the other side of the inequality sign. Solve \(2x - 5 < 5x - 11\) for x by subtracting \(2x\) from each side to get: \(-5 < 3x - 11\)
02

Isolate x

Now, add 11 to both sides of the inequality to isolate the terms with x: \(-5 + 11 < 3x - 11 + 11\). This simplifies to \(6 < 3x\)
03

Solve for x

Now, divide each side of the inequality by 3 to solve for x: \(6 \div 3 < 3x \div 3\). This gives \(x > 2\)
04

Graph the solution

The solution to the inequality is \(x > 2\). This can be represented on a number line by placing an open circle at 2 and shading in everything to the right of 2 to show all numbers greater than 2.

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