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In this lesson, we will learn how to solve compound linear inequalities by applying inverse operations.

Q1:

Find all values of π₯ that satisfy β 2 0 β π₯ β€ 3 π₯ + 2 < 1 8 β 2 π₯ . Write your answer as an interval.

Q2:

Find all values of π₯ that satisfy 3 + 3 π₯ β€ 7 π₯ β 3 β€ 5 + 2 π₯ . Write your answer as an interval.

Q3:

Find all values of π₯ that satisfy β 1 1 β π₯ < 6 π₯ β 3 β€ β 3 β π₯ . Write your answer as an interval.

Q4:

Find the solution set of the inequality in . Give your answer in interval notation.

Q5:

Solve β 5 β 3 π₯ β₯ 4 and π₯ + 3 < β 5 .

Q6:

Find the solution set of the inequality | β 1 | < 3 π₯ β 8 β€ 7 in β . Give your answer in interval notation.

Q7:

Find the solution set of β 1 2 < β π₯ β€ 1 2 . Write your answer as an interval.

Q8:

Find the solution set of β 6 > 2 π₯ + 1 0 > β 1 6 , where π₯ β β .

Q9:

Find the solution set of the inequality 4 > β 3 π₯ + 5 > 2 in β . Give your answer in interval notation.

Q10:

How many integer solutions does the inequality 1 2 < π₯ < 3 4 have?

Q11:

Find the solution set of the inequality 2 β€ 3 π₯ + 1 < 3 in β . Give your answer in interval notation.

Q12:

Find the solution set of the inequality 3 β 6 4 β€ π₯ β 9 β€ β 8 1 in β . Give your answer in interval notation.

Q13:

Given that π§ β β , solve the inequality 5 β₯ 6 π§ + 1 β₯ 4 .

Q14:

Find the solution set of the inequality β 4 < 5 π₯ β 5 β€ 5 in β . Give your answer in interval notation.

Q15:

Find the solution set of 5 β€ 2 π₯ + 3 β€ 7 given that π₯ β β .

Q16:

Solve 1 0 π₯ + 1 < π₯ β 8 and π₯ β 1 > β 5 .

Q17:

This number line describes the solution set to which of the following inequalities?

Q18:

Q19:

Q20:

Q21:

Which of the following is the set π΄ of all whole numbers π₯ such that π₯ + 3 < 6 ?

Q22:

Q23:

Find the solution set of the inequality β 3 < π₯ β€ 1 2 in β . Give your answer in interval notation.

Q24:

If β 9 β€ π₯ < 5 , where π₯ β β , then what interval does 1 0 π₯ lie in?

Q25:

Find the solution set of 7 < π₯ β 1 2 < 1 1 , where π₯ β β .

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