Exercises for Question Type 4: Solving absolute value equations by considering all possible conditions

Question 1

Skill question

Solve the equation $∣ x^{2} - 9∣ + ∣ x - 3∣ = 6$ .

[8]

Question 2

Skill question

Solve the equation $∣ x^{2} - 5 x + 6∣ + ∣2 x - 3∣ = 4$ .

[7]

Question 3

Skill question

Solve the equation $∣ x^{2} - 4∣ + ∣ x + 1∣ = 5$ .

[7]

Question 4

Skill question

Solve the equation $∣ x^{2} - 4 x ∣ = ∣2 x - 4∣$ .

[5]

Question 5

Skill question

Solve the equation $∣2 x + 1∣ = 7$ .

[3]

Question 6

Skill question

Solve the equation $∣ x^{2} - 4∣ + ∣ x^{2} - 5 x + 6∣ = 7$ .

Question 7

Skill question

Solve the equation $∣ x^{2} - 4∣ = 6$ .

[4]

Question 8

Skill question

Solve the equation $∣ x - 3∣ = 5$ .

[3]

Question 9

Skill question

Solve the equation $∣ x - 2∣ + ∣ x + 2∣ = 6$ .

[5]

Question 10

Skill question

Solve the equation $∣3 x - 2∣ + ∣ x - 1∣ = 4$ .

[5]

Question 11

Skill question

Solve the equation $∣ x^{2} - 1∣ = ∣ x - 1∣ + 2$ .

[7]

Question 12

Skill question

Solve the equation $∣ x + 1∣ + ∣ x - 2∣ + ∣ x - 4∣ = 6$ .

[6]

IB Mathematics Analysis and Approaches Question Type 4: Solving Absolute Value Equations by Considering All Possible Conditions Exercises