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Chapter 7: Problem 18

Graph each linear inequality. \(x \leq-4\)

Short Answer

Expert verified
The solution to the inequality \(x \leq -4\) consist of the number -4 and all numbers to its left on the number line. This is visually represented by a solid circle at -4, and a line extending to the left from -4.

Step by step solution

01

Identify the inequality type

The given inequality is \(x \leq -4\). In this case, the inequality shows 'less than or equal to', which means every value less than or equal to -4 will satisfy the inequality. Here, the equal-to part signifies that -4 is included in the solutions, and so we'll represent that on the graph with a closed circle.
02

Establish a number line

Draw a horizontal line to represent a number line. Mark it at appropriate intervals. Make sure to include -4 and numbers both less than and greater than -4.
03

Graph the inequality

The point -4 on the number line should be represented by a closed circle as it is included in the solution set. For the inequality \(x \leq -4\), all x-values to the left of -4 which are lesser than -4, are also solutions to the inequality. Therefore, draw a line from the -4 mark to the left, representing all values that satisfy the inequality. It is recommended to use a different color or a dotted line for this step.

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