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Chapter 5: Q8. (page 322)

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

The solution set to the inequalityy鈮�xincludes theboundary炉.

Short Answer

Expert verified

The given sentence is True.

Step by step solution

01

Step 1. Define half-plane and boundary.

When the inequality is converted into equality, equation is obtained and when the equation is graphed then the equation defines the boundary and the boundary divides the coordinate plane into two half planes.

If the boundary is included in the graph of an inequality then the solution is called closed half-plane.

If the boundary is not included in the graph of an inequality then the solution is called open half-plane.

02

Step 2. State whether the given sentence is true or false.

The given sentence is true because the inequality isy鈮�x and in the inequality, equal sign is there and therefore when the inequality is graphed, it includes the boundary therefore the solution is closed half-plane.

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Most popular questions from this chapter

Define a variable, write an inequality, and solve each problem. Check your solution.

Twice a number increased by 3 is less than the number decreased by 4.

Solve each inequality. Then graph it on a number line.

x+8鈮�3

Solve each inequality. Check your solution.

2m鈮�鈭�10

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

The boundary is the graph of the equation of the line that defines the edge of each half-plane.

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Which expression below illustrates the Associative property?

Fabc=bac

G2(x鈭�3)=2x鈭�6

H(p+3)鈭�t=p+(3鈭�t)

J5+(鈭�5)=0
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