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In this lesson, we will learn how to solve multistep inequalities.

Q1:

Find all values of π₯ that satisfy 4 + π₯ < 2 π₯ β 5 < 7 + π₯ . Write your answer as an interval.

Q2:

Solve the inequality 5 β 1 2 π₯ β₯ 1 0 for π₯ .

Q3:

Solve the following inequality: π 5 + 1 < 6 .

Q4:

Given that π₯ β β€ , write the solution set of 2 π₯ β 6 β€ π₯ β 1 .

Q5:

Determine the solution set of given that .

Q6:

Suppose that π > π . Solve the inequality π ( π₯ β 5 ) β₯ π π₯ + 3 π .

Q7:

The solution set of the inequality β 4 7 β€ π₯ β 1 0 7 β€ 4 is [ π , π + π ] , where π and π are real numbers. What is the value of π ?

Q8:

Solve the inequality 1 0 π₯ + 1 6 β€ 8 ( π₯ β 1 9 ) in β .

Q9:

Solve the inequality 6 π₯ β 2 7 4 β₯ 4 5 in β .

Q10:

If π§ + 1 β€ β 9 , then β π§ .

Q11:

Find the solution set of the inequality β 6 π₯ β 1 7 < β 5 π₯ + 4 β€ β 6 π₯ β 3 in β . Give your answer in interval notation.

Q12:

Solve the inequality 7 π₯ β 8 π₯ + 1 1 β€ 8 in β .

Q13:

Given that π§ β β , solve the inequality β 4 ( π§ β 3 ) β ( β 4 π§ β 4 ) β€ β 3 ( 3 π§ β 1 ) .

Q14:

Find the solution set of 2 π₯ β 1 β€ β 9 given that π₯ β β .

Q15:

Find the solution set of the inequality 3 π₯ β€ β 9 π₯ β€ 1 2 + 3 π₯ in β . Give your answer in interval notation.

Q16:

Solve the inequality β 1 0 ( π₯ + 2 ) < 1 6 π₯ β 2 2 in β .

Q17:

Solve the inequality β 4 ( π¦ + 4 ) β 1 2 < β 5 0 β ( 4 7 β π¦ ) in β .

Q18:

Solve the inequality 1 7 + 7 ( π₯ β 1 3 ) β₯ π₯ + 4 4 in β .

Q19:

Solve the inequality 9 π₯ β 3 ( β 7 π₯ + 9 ) < β 7 ( β 9 + π₯ ) β 2 in β .

Q20:

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

Q21:

Solve the inequality π₯ 8 β 8 β€ β 7 π₯ β 2 9 in β .

Q22:

Determine the solution set of β 7 π₯ + 5 > β 9 given that π₯ β β€ .

Q23:

If 4 π₯ + 7 β€ β 1 , then 5 π₯ β€ .

Q24:

Find the solution set of the inequality β 1 4 π₯ β 5 2 β€ β 1 8 π₯ in β . Give your answer in interval notation.

Q25:

Solve the inequality β 6 ( π₯ β 3 ) β₯ 4 ( π₯ + 5 ) in β .

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