Lesson Worksheet: Exponential Inequalities Mathematics • 10th Grade

In this worksheet, we will practice solving the exponential inequalities whose bases can all be converted to the same value.

Q1:

It is known that 16 is in the interval [0.25,0.5]. In what interval does 𝑥 lie?

  • A[−0.25,0.5]
  • B[−0.5,−0.25]
  • C[−0.5,0.5]
  • D[0.25,0.5]
  • E[−0.5,0.25]

Q2:

If 13>13, which of the following must be true about 𝑥 and 𝑦?

  • A𝑥=𝑦
  • B𝑥>𝑦
  • C𝑦>𝑥

Q3:

Find the values of 𝑥 that satisfy the following inequality: 4>8.

  • A𝑥<2
  • B𝑥<1
  • C𝑥>2
  • D𝑥>1
  • E𝑥<0

Q4:

Find all the values of 𝑥 that satisfy the following inequality: 2>2.

  • A𝑥<1
  • B𝑥>3
  • C𝑥<3
  • D𝑥<0
  • E𝑥>1

Q5:

Suppose that 𝑎<𝑥<𝑏 is the solution of the following inequality: 13>19. Find 𝑏−𝑎.

Q6:

Find all the values of 𝑥 that satisfy the following inequality: 1≥4.

  • A𝑥≤4
  • B𝑥≥−94
  • C𝑥≤−94
  • D𝑥≥−4
  • E𝑥≤−4

Q7:

Find all the values of 𝑥 that satisfy the following inequality: (0.01)≥110.

  • A𝑥≥−5
  • B𝑥≥−2
  • C𝑥≤−2
  • D𝑥≥5
  • E𝑥≥−53

Q8:

Find all the values of 𝑥 that satisfy the following inequality: −423≤−9.

  • A𝑥≤−3
  • B𝑥≥−3
  • C𝑥≥1
  • D𝑥≤1
  • E𝑥≥3

Q9:

Find all the values of 𝑥 that satisfy the inequality (0.01)<1.

  • A𝑥>5
  • B𝑥>2
  • C𝑥<5
  • D𝑥<92
  • E𝑥>92

Q10:

Find all the values of 𝑥 that satisfy the following inequality: 2≤14.

  • A𝑥≤2
  • B𝑥≥2
  • C𝑥≤4
  • D𝑥≤−2
  • E𝑥≥4

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