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In this lesson, we will learn how to solve quadratic inequalities in one variable algebraically.

Q1:

Solve the inequality β 2 π₯ + π₯ β₯ β 6 2 .

Q2:

Solve the inequality 6 π₯ β 5 π₯ β₯ 4 2 .

Q3:

Solve the inequality 4 π₯ + 8 π₯ β₯ 5 2 .

Q4:

Which of the following describes the solution set of the inequality π₯ β 7 π₯ + 1 2 > 0 2 ?

Q5:

Write the interval describing all solutions to the inequality 3 0 + 1 3 π₯ β π₯ > 0 2 .

Q6:

Find all solutions to the inequality ( π₯ + 4 ) + ( π₯ + 1 ) ( π₯ β 1 6 ) < 0 2 . Write your answer as an interval.

Q7:

A mobile phone company has the following cost and revenue functions: πΆ ( π₯ ) = 8 π₯ β 6 0 0 π₯ + 2 1 5 0 0 2 and π ( π₯ ) = β 3 π₯ + 4 8 0 π₯ 2 . State the range for the number of mobile phones they can produce while making a profit. Round your answers to the nearest integer that guarantees a profit.

Q8:

Find the interval describing all solutions to the inequality π₯ β€ 4 2 .

Q9:

Given π = 3 π₯ β 9 π₯ + 6 2 , find the solution set of the inequality π ( π₯ ) < 0 by determining the sign of π .

Q10:

Write the interval describing all solutions to the inequality β π₯ β 2 π₯ + 1 6 8 β₯ 0 2 .

Q11:

Solve the inequality ( π₯ β 5 ) ( π₯ β 7 ) β₯ β 5 π₯ + 3 5 .

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