Problem 59 Graph each compound inequality. ... [FREE SOLUTION]

Chapter 9: Problem 59

Graph each compound inequality. \(y<4\) or \(x \geq-3\)

Short Answer

Expert verified

To graph the compound inequality \(y < 4\) or \(x \geq -3\), first graph each individual inequality. For \(y < 4\), draw a dashed horizontal line at \(y = 4\) and shade below the line. For \(x \geq -3\), draw a solid vertical line at \(x = -3\) and shade to the right of the line. The solution set is the union of both shaded regions, representing the points that satisfy either inequality.

Step by step solution

Graphing the first inequality \(y < 4\)#

To graph the inequality \(y < 4\), first, draw the horizontal line \(y = 4\). Since the inequality is strictly less than, we'll use a dashed line, indicating that the points on the line are not included in the solution. Then, shade the region below the line, which corresponds to all points with a y-coordinate less than 4.

Graphing the second inequality \(x \geq -3\)#

To graph the inequality \(x \geq -3\), first, draw the vertical line \(x = -3\). Since the inequality has an equal sign, we'll use a solid line, indicating that the points on the line are included in the solution. Then, shade the region to the right of the line, which corresponds to all points with an x-coordinate greater than or equal to -3.

Graphing the compound inequality#

Since the compound inequality consists of two separate inequalities connected by "or", we must graph both inequalities on the same coordinate plane and find the region where either of the inequalities holds true. In this case, the shaded region below the line \(y = 4\) (dashed line) and the shaded region to the right of the line \(x = -3\) (solid line) together form the solution for the compound inequality. Since the inequalities are connected by "or", the union of both shaded regions represents the solution set for the compound inequality.

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91影视

Graph each compound inequality. \(y<4\) or \(x \geq-3\)

Short Answer

Step by step solution

Graphing the first inequality \(y < 4\)#

Graphing the second inequality \(x \geq -3\)#

Graphing the compound inequality#

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