Problem 22 Graph the inequality. \(x>-... [FREE SOLUTION]

Chapter 6: Problem 22

Graph the inequality. \(x>-2\)

Short Answer

Expert verified

The graph of the inequality \(x>-2\) is an open circle at -2 on the number line, and an arrow pointing to the right from -2, indicating that all numbers greater than -2 are the solution to the inequality.

Step by step solution

Understand the inequality

Here, the inequality \(x>-2\) implies that all the numbers greater than -2 are the solutions. Since no 'equal to' symbol is there, -2 itself is not included in the solution.

Draw the number line

Draw a number line and mark -2 on the number line.

Graph the inequality

Draw an open circle at -2 indicating that -2 is not included in the solution. Arrow on the number line should point to the right from -2, indicating that all numbers to the right of -2 are the solution.

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Key Concepts

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

Number Line

A number line is a visual tool used to represent real numbers and their order. It's a horizontal straight line with numbers placed at intervals along it. Typically, zero is marked near the center, with positive numbers extending to the right and negative numbers extending to the left. This makes it a perfect way for us to illustrate inequalities like the one in our exercise, \(x > -2\).

In this context, drawing a number line helps us visually interpret the range of numbers we are dealing with. To start:

Draw a straight horizontal line.
Select a point on this line to represent zero.
Count spaces to the left for negative numbers and to the right for positive numbers.
Label a few points above the line for clarity, such as -2, 0, 1, 2, etc.

Once you've done this, you have a setup to mark specific values and interpret inequalities easily. For \(x > -2\), you'd label -2 and focus on the section to the right of it.

Open Circle

In graphing inequalities on a number line, the open circle is a key symbol used to indicate that a number is not included in the solution set. When you graph \(x > -2\), you need a way to show that -2 itself is not part of the solutions. This is where an open circle comes in handy.

To use an open circle:

Find the point on the number line that corresponds to the number in question, which is -2 in our exercise.
Draw a circle around this point. Since -2 is not part of the solution set in \(x > -2\), the circle should be left open, meaning it is not filled in.

This visual marker clearly communicates that while the number is a boundary or reference point, it is not included in the actual set of solutions for the inequality.

Solution Set

The solution set refers to all the values that satisfy our inequality. For \(x > -2\), the solution set includes every number greater than -2. This solution set is expressed on the number line as all the points lying to the right of the open circle at -2.

To illustrate the solution set:

Use an arrow starting from the open circle at -2, extending to the right. This indicates that all points in that direction are solutions.
Remember, no upper boundary is necessary unless there is a restriction in the inequality.

The arrow effectively communicates an infinite set of numbers, stretching towards positive infinity. Each point along the arrow represents a possible solution, reinforcing that any number greater than -2 is acceptable.

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91影视

Graph the inequality. \(x>-2\)

Short Answer

Step by step solution

Understand the inequality

Draw the number line

Graph the inequality

Key Concepts

Number Line

Open Circle

Solution Set

One App. One Place for Learning.

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