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Chapter 9: Q 371 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.

x2+3x鈭�4鈮�0

Short Answer

Expert verified

The solution in interval notation is 鈥�(-鈭�鈥�,鈥�-4]鈭�鈥�[1,鈥�鈭�鈥�)

Step by step solution

01

Step 1. Given information

x2+3x鈭�4鈮�0

02

Step 2. Solve algebraically 

Write the quadratic inequality in standard form.

x2+3x鈭�4鈮�0

Multiply both sides of the inequality by 鈭�1.

Remember to reverse the inequality sign

-x2-3x+4鈮�0

Determine the critical points by solving

the related quadratic equation.

-x2-3x+4=0x2+3x-4=0

Write the Quadratic Formula.
x=-b卤b2-4ac2ax=-3卤52x=1andx=-4

Use the critical points to divide the number line into intervals.

Test numbers from each interval in the original inequality

03

Step 3. Solution

Determine the intervals where the inequality is correct. Write the solution in interval notation.

x2+3x鈭�4鈮�0in the middle interval 鈥�(-鈭�鈥�,鈥�-4]鈭�鈥�[1,鈥�鈭�鈥�)

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