1. What are Algebraic Equations?
A mathematical statement in which two expressions are set equal to each other is called an algebraic equation. These equations are consistent with variables, coefficients and constants. In daily life we often use algebraic equations for example while deciding how many of each brand of candy to buy at the store with limited funds or working out friend’s real age for her hints.
1.1 How to solve algebraic equations?
Steps to solve algebraic equations:
- To solve algebraic equations using the balance method, perform the same operation (addition, subtraction, multiplication or division) on each side of the equation.
- Use the balance method to get variables on one side and numbers on the other side of the equation.
2. Example Questions on Algebraic Equations
2.1 One-Step Equations:
Example:
Solve the equation y + 2 = 8.
Solution:
y + 2 = 8
y + 2 - 2 = 8 - 2 (Separate y by subtracting each side by 2)
So, y = 6
2.2 Two-Step Equations:
Example:
Solve the equation 10x + 7 = 12
Solution:
Solving equation 10 x + 7 = 12 using balance method
Add -7 to both the sides of the equation.
10x + 7 - 7 = 12 - 7
10x = 5
To find x, divide both sides of the equation by 10.
x = 5 ÷ 10 = 0.5
2.3 Multi-Step Equations:
Multi-step equations are of three types.
- Equations with unknowns on both sides
- Equations with brackets
- Equations with fractions
Example:
Solve the equation 6(m+2) = 10m - 8
Solution:
6(m + 2) = 10m - 8
Expand the brackets on the left side,
6m + 12 = 10m - 8
The above equation has unknown variable on both the sides, subtract the unknown which has a smaller number in front of it.
6m + 12 - 6m = 10m - 8 - 6m (6 is less than 10, so subtract 6m from each side)
12 = 4m - 8
12 + 8 = 4m - 8 + 8 (Adding 8 on each side)
20 = 4m
20 ÷ 4 = 4m ÷ 4 (Divide each side by 4)
2 = m or m = 2
