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Chapter 6: Problem 59

Solve each inequality and graph the solution set on a number line. \(6

Short Answer

Expert verified
The solution set for the inequality \(6<x+3<8\) is \(3 < x < 5\), which can be represented on the number line as an open interval between 3 and 5.

Step by step solution

01

Split the Inequality

First, break the compound inequality into two simple inequalities. This gives \(6 < x+3\) and \(x+3 < 8\)
02

Solve the Inequalities

Now that we have the two inequalities, we can solve them individually by subtracting 3 from all parts of the inequalities. This gives \(x > 3\) from \(6 < x+3\) and \(x < 5\) from \(x+3 < 8\)
03

Graphing the Solutions

The number line is drawn, marking points corresponding to 3 and 5. An open circle is drawn at x = 3 (since x can't be equal to 3) and another open circle at x = 5 (since x can't be equal to 5 too). Because x is greater than 3 and less than 5, the region between these two points on the number line is shaded.

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Most popular questions from this chapter

Solve the quadratic equations by factoring. \(x^{2}-4 x=21\)

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