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Magazine Chapter 2: Q.2.104 (page 175)
Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
Short Answer
The solution in interval notation is
The solution on number line is:
Step by step solution
Step 1. Given Information
Given inequality is
The inequality is to be solved, the solution is to be graphed on the number line, and the solution is to be written in interval notation.
Step 2. Solving the inequality
When an inequality is multiplied or divided by a negative number, the inequality sign changes direction.
Isolating the variable in the inequality:
In an interval notation, a round brackets indicates that the extreme value is excluded and a square bracket indicates that the extreme value is included.
Hence the solution in the interval notation is
Step 3. Graphing the inequality
On a number line, if the inequality is less than or greater than then a hollow dot is used to indicate that the number is not included. If the inequality is less than equals or greater than equals then a solid dot is used to indicate that the number is included.
Graphing the interval on a number line:
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