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Chapter 2: Q. 8 (page 126)

Solve the inequality. Graph the solution set.

2x-5<3

Short Answer

Expert verified

The solution set of the given inequality is:

1,4

The graph of the solution set is given as:

Step by step solution

01

Step 1. Given information

The given equation is 2x-5<3

02

Step 2. Open the modulus function

We know that, from the principle of absolute value,for x<a, we have:

-a<x<a

Similarly, for 2x-5<3, we have:

-3<2x-5<3

03

Step 3. Solving the inequality

Solving the inequality using properties, we get

-3<2x-5<3-3+5<2x<3+52<2x<81<x<4

04

Step 4. Verify the solution set

Substituting the value between 1and 3in the inequality, we get:

2x-5<32脳2-5<34-5<3-1<31<3

This is true.

Hence, the solution set of the given inequality is1<x<4

05

Step 5. Graph the solution set

The graph of the solution set is given as:

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Most popular questions from this chapter

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

A rectangle has one corner in quadrant I on the graph of y=16-x2, another at the origin, a third on the positive y-axis and the fourth on the positive x-axis. See the figure.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Alargest?

Suppose that the x-intercepts of the graph of y=f(x)are-5and 3.

(a) What are the x-intercepts of the graph of y=f(x+2)?

(b) What are the x-intercepts of the graph of y=f(x-2)?

(c) What are thex-intercepts of the graph of y=4f(x)?

(d) What are thex-intercepts of the graph of y=f(-x)?

In Problems 7鈥�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

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1
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