Problem 30 Graph the inequality. \(x<-0... [FREE SOLUTION]

Chapter 6: Problem 30

Graph the inequality. \(x<-0.5\)

Short Answer

Expert verified

The graph consists of a dotted vertical line at x = -0.5. The area to the left of this line, representing all the possible x values that are less than -0.5, is shaded.

Step by step solution

Identify inequality

The inequality is \(x<-0.5\). We will graph the line for x = -0.5 and indicate the areas where x is less than -0.5.

Draw the line

Firstly, draw a vertical line at x = -0.5. This would be a dotted line since x is strictly less than -0.5, which means that -0.5 is not included in the solution.

Shade the correct area

The inequality states that x should be less than -0.5. Therefore, we shade the area to the left of the line we have just drawn, indicating all the possible values that x can be according to the inequality.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vertical Lines in Graphing

When you're graphing an inequality like \( x < -0.5 \), one of the first steps is to draw a vertical line. Vertical lines differ from horizontal lines because they rise up and down the y-axis, crossing the x-axis at a constant x-value. In this exercise, that value is -0.5.

To draw this vertical line, just locate -0.5 on the x-axis and draw a line parallel to the y-axis through this point. It's important to be precise with placing your line exactly at x = -0.5, as this line sets the boundary for the inequality.

Dotted Line for Strict Inequalities

When graphing inequalities, it's crucial to show whether the boundary is included in the solution or not. In inequalities like \( x < -0.5 \), the value -0.5 isn't part of the solution set, meaning it's a strict inequality.

To represent this visually, use a dotted line instead of a solid line. Dotted lines tell us that points on the line are not part of the solution set, distinguishing strict inequalities from inclusive ones. Always remember:

Solid line: points on the line are included (\( \leq \) or \( \geq \)).
Dotted line: points on the line are not included (\( < \) or \( > \)).

Shading Graph Regions

In graphing inequalities, shading the correct region is essential to depict all possible solutions. For the inequality \( x < -0.5 \), once your vertical dotted line is in place, you need to shade the region representing all x-values less than -0.5.

To do this, shade the area to the left of the vertical line. This region visually shows all the x-values satisfying the inequality. When shading:

Ensure your shading clearly defines the boundary.
It should extend infinitely in the direction specified by the inequality.

This step highlights the set of solutions in an easy-to-understand visual format, making it clear and precise.

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91影视

Graph the inequality. \(x<-0.5\)

Short Answer

Step by step solution

Identify inequality

Draw the line

Shade the correct area

Key Concepts

Vertical Lines in Graphing

Dotted Line for Strict Inequalities

Shading Graph Regions

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