This document provides instructions and examples for solving various types of equations, including: 1. Linear equations with one variable such as 4m - 2 = 6. 2. Radical equations where the radicand contains an unknown variable, along with guidelines for solving such equations by isolating radical terms and applying the principle of powers. 3. Sample radical equations are provided for practice, including x - 1 = 2, 3x + 2 = 3, and x + 1 = 3. 4. Readers are then instructed to practice solving similar equations on their own.

1. Preparatory Activity

2. Solve the given equation.
1. 4𝑚 − 2 = 6
2.
𝑋
2
− 3 = 1
3.
3
2
+ 𝑥 = 2
4.
4
5
𝑥 =
27
5
5. 3𝑥 + 5 = 35
6. 2 𝑥 − 7 = 3 𝑥 + 1

3. EQUATIONS
WITH RADICALS

4. A radical equation is an equation whose
radicand contains an unknown variable.
 The following are examples of radical equations:
𝑥 − 1 = 5
2 𝑥 + 1 = 2
3
𝑥 = 1 + 𝑥

5. Guidelines in Solving
Radical Equations
Place or isolate one of the radical terms.
Apply the principle of powers.
If the radical remains, perform steps 1 and 2
again.
Check for possible solutions.

6. LETS TRY TO SOLVE THE FOLLOWING:
1. 𝑥 − 1 = 2
2. 3𝑥 + 2 = 3
3. 𝑥 + 1 = 3
4.
3
𝑥 + 5 = 2
5. 𝑥 + 5 − 2 𝑥 = 0

7. More Examples:
1. 3𝑥 + 4 = 8
2. 2𝑧 + 3 + 5 = 0
3.
3
𝑎 − 1 = 4
4. 𝑚2 − 4𝑚 + 9 = 𝑚 − 1

8. ITS YOUR TURN!
Warm-Up Practice
Page 32
ACTIVITY A
ODD items ONLY