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Chapter 6: Problem 19

Solve each inequality and graph the solution set on a number line. \(4 x<20\)

Short Answer

Expert verified
The solution set to the inequality \(4x<20\) is \(x < 5\). On a number line, it will be represented by an open circle at 5 with the line moving to the left of 5, showing all values smaller than 5.

Step by step solution

01

Divide Both Sides by Coefficient of Variable

To isolate \(x\), divide the inequality by the coefficient of \(x\), which is 4 in this case. Thus, \(4x/4 < 20/4\).
02

Simplification

After division, simplify the inequality to get \(x < 5\).
03

Graph the Solution on Number Line

Draw a number line ranging from 0 to 10. The solution to this inequality is \(x < 5\), which means the solution set consists all real numbers less than 5. In the number line, plot an open circle at 5 to indicate this value is not included in the solution set. Then, draw a line to the left of 5 to show all numbers less than 5 are part of the solution.

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Most popular questions from this chapter

Solve each equation by the method of your choice. \(\frac{x^{2}}{3}-\frac{x}{2}-\frac{3}{2}=0\)

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