Lessons Grade 7

Chapter 5

Chapter 5: Algebra

5.1 Introduction to Algebra

Algebra involves using letters (variables) to represent unknown numbers or quantities. The goal is to solve for the variable.

Example: In the equation x+3=7x + 3 = 7x+3=7, the goal is to solve for xxx.

5.2 Solving Simple Equations

To solve an equation, isolate the variable on one side.

Example:

x+4=10x + 4 = 10x+4=10

Subtract 4 from both sides:

x=6x = 6x=6

5.3 Expressions and Like Terms

An algebraic expression is a combination of variables, numbers, and operations. Like terms are terms that have the same variable raised to the same power.

Example: In the expression 3x+5x3x + 5x3x+5x, the terms 3x3x3x and 5x5x5x are like terms and can be combined to give 8x8x8x.

Exercises

Exercise 1: Solve the following simple equations:

x+5=12x + 5 = 12x+5=12

y−7=14y - 7 = 14y−7=14

2x=102x = 102x=10

3y+4=163y + 4 = 163y+4=16

5x−3=175x - 3 = 175x−3=17

Exercise 2: Simplify the following algebraic expressions:

4x+3x4x + 3x4x+3x

7y+2y−5y7y + 2y - 5y7y+2y−5y

3a−4a+2a3a - 4a + 2a3a−4a+2a

6m+2n−4m+n6m + 2n - 4m + n6m+2n−4m+n

5b+6b−3b5b + 6b - 3b5b+6b−3b

Take your time. There is no need to be fast. I hope that you will solve it.