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In this lesson, we will learn how to solve inequalities that contain absolute values.

Q1:

Find the solution set of the inequality | π₯ + 4 | < 9 .

Q2:

Find algebraically the solution set of the inequality .

Q3:

Find algebraically the solution set of the inequality | 6 β π₯ | < 3 .

Q4:

Find the solution set of the inequality | π₯ β 6 | β₯ 7 .

Q5:

A body was moving with a uniform velocity of magnitude 5 cm/s from the point π΄ to the point πΆ passing through the point π΅ without stopping. The distance between the body and the point π΅ is given by π ( π‘ ) = 5 | 8 β π‘ | , where π‘ is the time in seconds, and π is the distance in cm. Determine the distance between the body and the point π΅ after 5 seconds and after 11 seconds.

Q6:

A body moved from position π΄ to position πΆ passing through position π΅ with a uniform velocity of 3 cm/s and without stopping. If the distance between the body and position π΅ is given by π ( π‘ ) = 3 | 7 β π‘ | , where π‘ is the time in seconds, and π is the distance in centimetres, determine the time interval during which the body is less than 9 cm from π΅ .

Q7:

Find algebraically the solution set of the inequality | 8 β π₯ | > 1 7 .

Q8:

A factory produces cans with weight π₯ grams. To control the production quality, the cans are only allowed to be sold if | π₯ β 1 8 3 | β€ 6 . Determine the heaviest and the lightest weight of a can that can be sold.

Q9:

Which of the following represents the interpretation for | β 3 . 3 β π | > 5 ?

Q10:

Find the solution set of the inequality | π₯ β 3 | β€ 7 .

Q11:

Q12:

Find the solution set of the inequality | π₯ β 8 | > 2 .

Q13:

Suppose that | 2 π₯ β π | < 2 and π > 6 . Which of the following is true?

Q14:

Suppose π < 0 < π . If π > 2 , which of the following statements is true?

Q15:

Solve | π₯ β 6 | β€ 5 .

Q16:

Solve π₯ β 4 < | 2 β π₯ | .

Q17:

What is the interval which represents the set of all real numbers that are less than or equal to | 6 | ?

Q18:

Which of the following is true?

Q19:

Find algebraically the solution set of the inequality | β 3 β 2 π₯ | + | 2 π₯ + 3 | < 2 6 .

Q20:

Find algebraically the solution set of the inequality | 3 β π₯ | + | 2 π₯ β 6 | β₯ 5 7 .

Q21:

Use the graph to find the solution set of the inequality π ( π₯ ) β₯ π ( π₯ ) .

Q22:

Find the solution set of the inequality | π₯ + 1 | < 6 .

Q23:

Find the solution set of the inequality | π₯ β 2 | < 4 .

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