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Chapter 6: Problem 14

Solve each inequality and graph the solution set on a number line. \(x+1<5\)

Short Answer

Expert verified
The solution to the inequality \(x+1<5\) is \(x<4\). The solution set can be graphed on a number line as an open interval (-infinity, 4).

Step by step solution

01

Solve the Inequality

Subtract 1 from both sides of the inequality. This gives \(x+1-1<5-1\), which simplifies to \(x<4\).
02

Graph the Solution Set on a Number Line

Draw a number line with 0 in the middle and mark the point equivalent to the integer part of 4 on the number line. Since the solution to the inequality is \(x<4\), the interval on the number line which represents the solution will be to the left side of 4. Color that part of the line in to represent all numbers that are less than 4. Put an open circle on 4 to show that 4 itself is not included in the solution set.

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