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Chapter 3: Q. 11 (page 171)

In problems 7-22, solve the inequality.

x2-9<0

Short Answer

Expert verified

The solution set is (-3,3).

Step by step solution

01

Step 1. Given Information

Given inequality isx2-9<0.

02

Step 2. Find the vertex and intercepts

  • The value of f(0)=-9.
  • So, the y-intercept is (0,-9).
  • Factor the equation.

(x-3)(x+3)=0

  • Equate the factors to 0.

x-3=0x=3x+3=0x=-3

  • So, the x-intercepts are (3,0),(-3,0).
  • The vertex of the parabola exists at -b2a=-02(1)=0
  • So, the vertex is (0,-9).
03

Step 3. Plot the graph

Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

04

Step 4. Find the solution set     

  • From the graph, it is observed that for x belonging to (-3,3), y<0.
  • So, the solution set of the given inequality is (-3,3).

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