PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.7, Problem 35E
Solution

To explain the role of equation solving in the process of solving an inequality.

The corresponding equation reveals the boundary of the solution set of the inequality.

Calculation:

In order to solve an inequality in two variables, the first thing to be done is to locate the boundary line of the inequality. If the inequality is strict, the boundary line is dashed and if the inequality is not strict, then use a solid line.

After plotting the boundary line by solving the corresponding equation, locate the shaded region by taking a test point.

For example, to solve the inequality, 2x+5y≥10 .

The corresponding equation for the given inequality is 2x+5y=10

The graph of the equation 2x+5y=10 with a solid line

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.7, Problem 35E , additional homework tip 1

The graph of the equation 2x+5y=10 divides the plane into two regions.

A test point in either region not on the graph of the equation 2x+5y=10

Substitute the value x,y=0,0 in the inequality 2x+5y≥10

  2x+5y≥1020+50≥100≥10

The statement is false.

The test point does not satisfy the inequality; so, all of the points in that region do not satisfy the inequality.

The region not containing 0,0 is the solution set for the given inequality.

Therefore, shade the region not containing the point 0,0 as the solution set of the inequality 2x+5y≥10

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.7, Problem 35E , additional homework tip 2

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Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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