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Chapter 6: Problem 53

Solve each inequality and graph the solution set on a number line. \(8 x+3>3(2 x+1)-x+5\)

Short Answer

Expert verified
The solution to the inequality is \(x > \frac{5}{3}\). This corresponds to an open interval \(\left(\frac{5}{3}, +\infty\right)\) on the number line.

Step by step solution

01

Simplify Both Sides of the Inequality

Expand and combine like terms on both sides of the inequality: \[ 8x + 3 > 3(2x + 1) - x + 5 \implies 8x + 3 > 6x + 3 - x + 5 \implies 8x + 3 > 5x + 8 \]
02

Collect like terms

Bring terms involving \(x\) to one side and constant terms to the other side to simplify the inequality further:\[ 8x - 5x > 8 - 3 \implies 3x > 5 \]
03

Isolate the Variable

Isolate \(x\) by dividing each side of the inequality by 3: \[ x > \frac{5}{3} \]
04

Graph the Inequality on the Number Line

To graph \(x > \frac{5}{3}\), locate \(\frac{5}{3}\) on the number line. Make an open circle at \(\frac{5}{3}\) since the inequality sign does not include equal to. Draw an arrow to the right of \(\frac{5}{3}\) showing that \(x\) can be any number greater than \(\frac{5}{3}\).

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Most popular questions from this chapter

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