Exercises

Irrational equations and inequalities

Problems to solve on your own. The final solution appears with the button below each problem; each exercise also has its own page, to share with the link.

1. Equation with a root and a constant

Solve the equation

3 x + 1 = 4.

Solution available to those who have unlocked the subject.

2. Equation with a root and an expression on the right-hand side

Solve the equation

x + 5 = x - 1.

Solution available to those who have unlocked the subject.

3. Equation with a second-degree radicand

Solve the equation

x^{2} + 5 x = 6.

Solution available to those who have unlocked the subject.

4. Equation with two roots

Solve the equation

4 x - 3 = x + 6 .

Solution available to those who have unlocked the subject.

5. Equation with two roots and a second-degree radicand

Solve the equation

x^{2} - 1 = 3 x + 3 .

Solution available to those who have unlocked the subject.

6. Equation with two roots and a constant

Solve the equation

x + 10 = 2 + x + 2 .

Solution available to those who have unlocked the subject.

7. Inequality with a root less than a constant

Solve the inequality

x + 3 < 3.

Solution available to those who have unlocked the subject.

8. Inequality with a root less than an expression

Solve the inequality

2 x - 1 \leq x - 2.

Solution available to those who have unlocked the subject.

9. Inequality with a root greater than a constant

Solve the inequality

x + 1 > 3.

Solution available to those who have unlocked the subject.

10. Inequality with a root greater than an expression

Solve the inequality

x + 6 > x .

Solution available to those who have unlocked the subject.

11. Equation and inequality with cube roots

Solve the equation and the inequality

3 3 x - 5 = 1 and 3 x + 4 < 2.

Solution available to those who have unlocked the subject.

12. Greater-than inequality with a second-degree radicand

Solve the inequality

x^{2} - 3 x \geq x - 2.

Solution available to those who have unlocked the subject.