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Chapter 9: Q. 374 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.
x2-4x+3>0

Short Answer

Expert verified

The solution in interval notation is (-鈭�,1)鈭�(3,鈭�).

Step by step solution

01

Step 1. Given information.

The given inequality is:

x2-4x+3>0

02

Step 2. Determine the critical points.

Change the inequality sign to an equal sign and then solve the equation.

x2-4x+3=0

Split the middle term.

x2-3x-1x+3=0x(x-3)-1(x-3)=0(x-1)(x-3)=0x=1,3

The two critical points 1 and 3 divide the number line is three intervals (-鈭�,1),(1,3),(3,鈭�).

03

Step 3. Determine the intervals where the inequality is correct.

Signs of each of the factors and the sign of the product are shown in the number line.

From the above number line it is clear that (x-1)(x-3)>0over the intervals (-鈭�,1)and (3,鈭�).

04

Step 4. Conclusion.

The solution in interval notation is (-鈭�,1)鈭�(3,鈭�).

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