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Chapter 2: Q. 7 (page 126)

Solve the inequality. Graph the solution set.

2-3x>6

Short Answer

Expert verified

The solution set of the given inequality is -∞,-43

The graph of the solution set is given as:

Step by step solution

01

Step 1. Given information

The given inequality is2-3x>6

02

Step 2. Solve the inequality

Using properties of inequalities, we get:

2-3x>6-3x>43x<-4[multiplybothsidesby-1]x<-43

03

Step 3. Verify the solution

Substituting the value less than -43i.e.,-53 in the inequality, we get:

2-3x>62-3×-53>62--5>67>6

This is true.

Hence the solution of the inequality is

x<-43

04

Step 4. Graph the solution set.

The graph of the solution set is given as:

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Most popular questions from this chapter

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

g(x)=12x

Exploration Graph y=x3,y=x5, and y=x7 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

True or False The independent variable is sometimes

referred to as the argument of the function.

Write the point–slope form of the line with slope 5 containing the point (3, -2).
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