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Chapter 6: Problem 7

Graph each set of real numbers on a number line. \(\\{x \mid x \leq 4\\}\)

Short Answer

Expert verified
The graph has a dot at 4 on the number line and an arrow pointing to the left, indicating the inclusion of all real numbers less or equal to 4.

Step by step solution

01

Understand the Inequality

The inequality \(x \leq 4\), is a way to describe a set of numbers that are less than or equal to 4. This array will include any number less than 4 and the number 4 itself.
02

Draw the Number Line

Draw a straight horizontal line. This line is called a number line. It should encompass the number 4 and some numbers less than it. Label the points on the line as whole numbers for simplicity. The point labeled '4' and any points to its left on the line represent the numbers which are in the described set.
03

Indicate on Number Line

Indicate 4 on the number line with a filled dot or a small solid circle because 4 is included in the set. To represent all the numbers less than 4, draw an arrow pointing to the left from the circle. This shows that the set includes all numbers less than 4.

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Most popular questions from this chapter

Solve the quadratic equations by factoring. \(x^{2}+x-42=0\)

Use FOIL to find the products. \((2 x-9)(7 x-4)\)

Solve the quadratic equations in Exercises \(37-52\) by factoring. \(x^{2}+8 x+15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-25 x-28\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.
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