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Chapter 8: Problem 9

Graph each inequality. $$x \leq 1$$

Short Answer

Expert verified
The graph of the inequality \(x \leq 1\) is a vertical line at \(x = 1\) with shading to the left of the line.

Step by step solution

01

Understand the inequality

The inequality is \(x \leq 1\). Here 'x' represents an unknown value and '1' is a constant. The inequality symbol is \(\leq\), which means 'less than or equal to'. Therefore, this inequality can be read as 'x is less than or equal to 1'.
02

Graph the inequality

To graph this inequality, begin by drawing a vertical line at \(x = 1\). Because the inequality is \(x \leq 1\), points on the line \(x = 1\) are included in the solution. Conventionally, this is represented by a solid line. To represent the other part of the inequality, '\(x\) is less than 1', shade to the left of the line \(x = 1\). This shows that every point to the left of the line fits the inequality.

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Most popular questions from this chapter

Expand: \(\log _{8}\left(\frac{\sqrt[4]{x}}{64 y^{3}}\right) .\) (Section 4.3, Example 4)

An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of \(x\) and \(y\) for which the maximum occurs. Objective Function Constraints $$ \begin{aligned} &z=5 x+6 y\\\ &\left\\{\begin{array}{l} {x \geq 0, y \geq 0} \\ {2 x+y \geq 10} \\ {x+2 y \geq 10} \\ {x+y \leq 10} \end{array}\right. \end{aligned} $$

will help you prepare for the material covered in the next section. Solve by the substitution method: $$\left\\{\begin{array}{l}{4 x+3 y=4} \\\\{y=2 x-7}\end{array}\right.$$

will help you prepare for the material covered in the next section. Graph \(x-y=3\) and \((x-2)^{2}+(y+3)^{2}=4\) in the same rectangular coordinate system. What are the two intersection points? Show that each of these ordered pairs satisfies both equations.

Will help you prepare for the material covered in the next section. In each exercise, graph the linear function. $$ f(x)=-2 $$
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