Worksheet: Inequalities and Interval Notation

In this worksheet, we will practice solving simple and compound linear inequalities and expressing their solutions using interval notation.

Q1:

Find all values of 𝑥 that satisfy 18𝑥+41. Write your answer as an interval.

  • A[3,14]
  • B(5,22]
  • C(3,14]
  • D[5,22]

Q2:

Find the solution set of the inequality 24𝑥14 in . Give your answer in interval notation.

  • A34,34
  • B14,54
  • C14,54
  • D14,54
  • E14,54

Q3:

Find the solution set of the inequality 2𝑥+623 in . Give your answer in interval notation.

  • A(0,2)
  • B[0,2)
  • C(0,2]
  • D{0,2}
  • E[0,2]

Q4:

Find the solution set of the inequality 𝑥20 in . Give your answer in interval notation.

  • A(,20]
  • B(20,)
  • C(,20)
  • D(20,)

Q5:

Find the solution set of the inequality 4𝑥1<5 in . Give your answer in interval notation.

  • A32,
  • B32,
  • C,32
  • D(1,)

Q6:

Find the solution set of the inequality 𝑥+25 in . Give your answer in interval notation.

  • A[3,)
  • B[7,)
  • C(3,)
  • D[3,]
  • E(3,]

Q7:

Find the solution set of the inequality 13𝑥+4>4 in . Give your answer in interval notation.

  • A83,1
  • B0,53
  • C83,1
  • D83,1
  • E83,1

Q8:

Find the solution set of the inequality 2<4𝑥3<2 in . Give your answer in interval notation.

  • A14,54
  • B54,14
  • C14,54
  • D14,54
  • E14,54

Q9:

Find the solution set of the inequality 515𝑥2<2 in . Give your answer in interval notation.

  • A[15,20)
  • B(15,20]
  • C[15,20]
  • D(15,20)

Q10:

Find the solution set of the inequality 5𝑥110<2𝑥+5<𝑥+32 in . Give your answer in interval notation.

  • A75,5125
  • B75,5125
  • C75,5125
  • D75,5125
  • E75,5125

Q11:

If 6<𝑥4, then what interval does 3𝑥5 lie in?

  • A(11,1]
  • B(18,20]
  • C[23,7)
  • D(23,7]

Q12:

Find the solution set of the inequality 22𝑥42 in . Give your answer in interval notation.

  • A[1,3]
  • B[3,1]
  • C{3,1}
  • D(3,1]
  • E(3,1)

Q13:

Find the solution set of the inequality 3<5𝑥+4<3 in . Give your answer in interval notation.

  • A75,15
  • B15,75
  • C75,15
  • D75,15
  • E75,15

Q14:

Find the solution set of the inequality 014𝑥+13 in . Give your answer in interval notation.

  • A[4,8]
  • B(4,8)
  • C(4,8]
  • D[4,8)

Q15:

Find all values of 𝑥 that satisfy 20𝑥3𝑥+2<182𝑥. Write your answer as an interval.

  • A112,165
  • B92,4
  • C112,4
  • D112,165
  • E112,165

Q16:

Find the solution set of 12<𝑥12. Write your answer as an interval.

  • A[12,12)
  • B(12,12)
  • C(12,12]
  • D{12,12}
  • E(12,12]

Q17:

Find the solution set of the inequality 48𝑥<2 in . Give your answer in interval notation.

  • A(12,4]
  • B(12,4)
  • C[12,4]
  • D[12,4)

Q18:

Find the solution set of the inequality |1|<3𝑥87 in . Give your answer in interval notation.

  • A[3,5)
  • B[2,5]
  • C(3,5]
  • D(2,5)
  • E{3,5}

Q19:

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

  • A13,1
  • B13,1
  • C13,1
  • D13,1
  • E3,73

Q20:

Find the solution set of the inequality 23𝑥+1<3 in . Give your answer in interval notation.

  • A13,23
  • B13,23
  • C1,43
  • D13,23
  • E1,43

Q21:

Find the solution set of the inequality 4<5𝑥55 in . Give your answer in interval notation.

  • A15,2
  • B15,2
  • C15,2
  • D15,2
  • E95,0

Q22:

Find the solution set of the inequality 17<𝑥<32 in . Give your answer in interval notation.

  • A(32,17]
  • B[32,17)
  • C[32,17]
  • D(32,17)

Q23:

Find the solution set of the inequality 3<𝑥12 in . Give your answer in interval notation.

  • A{3,12}
  • B(3,12]
  • C[3,12]
  • D[3,12)

Q24:

If 9𝑥<5, where 𝑥, then what interval does 10𝑥 lie in?

  • A[90,50)
  • B{9,5}
  • C{90,50}
  • D(90,50]
  • E[9,5)

Q25:

Find all the values of 𝑥 that satisfy 11<7𝑥+432. Give your answer in interval form.

  • A(7,28]
  • B(1,4]
  • C[1,4]
  • D(1,4)
  • E[7,28]

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