Lesson Notes By Weeks and Term v5 - Grade 7
Algebraic expressions and simple equations – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Algebraic expressions and simple equations – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 7
Term: 2nd Term
Week: 5
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Algebraic expressions and simple equations form the foundation for more advanced mathematical concepts. They are essential for problem-solving, critical thinking, and understanding quantitative relationships. In the South African context, these skills are vital for budgeting household expenses, managing small businesses, understanding financial literacy, and pursuing careers in STEM fields. This week, we will focus on simplifying algebraic expressions and solving simple equations, building a strong base for future algebraic studies.
2.1 Algebraic Expressions An algebraic expression is a combination of variables, constants, and mathematical operations (addition, subtraction, multiplication, and division).
Variable: A letter or symbol that represents an unknown value (e.g., x, y, a, b).
Constant: A fixed number with a known value (e.g., 3, -5, 0.25).
Coefficient: The number that multiplies a variable (e.g., in the term 3x, 3 is the coefficient).
Simplifying Algebraic Expressions: Simplifying involves combining "like terms." Like terms have the same variable raised to the same power. Constants are also considered like terms. We combine like terms by adding or subtracting their coefficients.
Example 1: Simplify 3x + 5y - x + 2y - 4 Identify like terms: 3x and -x are like terms; 5y and 2y are like terms; -4 is a constant term.
Combine like terms: (3x - x) + (5y + 2y) - 4 Simplify: 2x + 7y - 4 Example 2: Simplify 7a - 2b + 4a + 6 + b - 1 Identify like terms: 7a and 4a are like terms; -2b and b are like terms; 6 and -1 are like terms.
Combine like terms: (7a + 4a) + (-2b + b) + (6 - 1)
Simplify: 11a - b + 5 2.2 Simple Equations An equation is a mathematical statement that shows two expressions are equal. It contains an equals sign (=). A simple equation typically involves one variable and can be solved using inverse operations.
Solving Simple Equations: Solving an equation means finding the value of the variable that makes the equation true. We do this by isolating the variable on one side of the equation. We use inverse operations to "undo" the operations affecting the variable.
Remember: whatever you do to one side of the equation, you MUST do to the other side to maintain balance.
Addition and Subtraction: If a number is added to the variable, subtract it from both sides. If a number is subtracted from the variable, add it to both sides.
Multiplication and Division: If the variable is multiplied by a number, divide both sides by that number. If the variable is divided by a number, multiply both sides by that number.
Example 1: Solve for x: x + 5 = 12 Isolate x: Subtract 5 from both sides of the equation. x + 5 - 5 = 12 - 5 Simplify: x = 7 Check: Substitute x = 7 back into the original equation: 7 + 5 =
1
2. The equation is true, so x = 7 is the correct solution.
Example 2: Solve for y: 3y = 18 Isolate y: Divide both sides of the equation by 3. 3y / 3 = 18 / 3 Simplify: y = 6 Check: Substitute y = 6 back into the original equation: 3 6 =
1
8. The equation is true, so y = 6 is the correct solution.
Example 3: Solve for z: z - 4 = 9 Isolate z: Add 4 to both sides of the equation. z - 4 + 4 = 9 + 4 Simplify: z = 13 Check: Substitute z = 13 back into the original equation: 13 - 4 =
9. The equation is true, so z = 13 is the correct solution.
Example 4: Solve for a: a / 2 = 5 Isolate a: Multiply both sides of the equation by 2. (a / 2) 2 = 5 * 2 Simplify: a = 10 Check: Substitute a = 10 back into the original equation: 10 / 2 =
5. The equation is true, so a = 10 is the correct solution. Guided Practice (With Solutions)
Question 1: Simplify the expression: 4p + 2q - p + 5q - 3 Solution: Identify like terms: 4p and -p are like terms; 2q and 5q are like terms; -3 is a constant term.
Combine like terms: (4p - p) + (2q + 5q) - 3 Simplify: 3p + 7q - 3
Commentary: We grouped the 'p' terms and the 'q' terms together and then performed the addition/subtraction to simplify the expression. The constant term remains unchanged as there are no other constant terms to combine with.
Question 2: Solve for x: x - 8 = 3 Solution: Isolate x: Add 8 to both sides of the equation. x - 8 + 8 = 3 + 8 Simplify: x = 11 Check: Substitute x = 11 back into the original equation: 11 - 8 =
3. The equation is true.
Commentary: We used the inverse operation (addition) to undo the subtraction of 8 from 'x'. This isolates 'x' on one side, revealing its value.
Question 3: Solve for y: 2y + 1 = 9 Solution: Isolate the term with 'y': Subtract 1 from both sides of the equation. 2y + 1 - 1 = 9 - 1 2y = 8 Isolate y: Divide both sides of the equation by 2. 2y / 2 = 8 / 2 Simplify: y = 4 Check: Substitute y = 4 back into the original equation: 2 4 + 1 = 8 + 1 =
9. The equation is true.
Commentary: This question involves two steps. First, we subtract to isolate the term with 'y', then divide to isolate 'y' itself. Remember to perform the operations in the correct order.
Question 4: Simplify the expression: 6m - 3n + 2m - n + 4 Solution: Identify like terms: 6m and 2m are like terms; -3n and -n are like terms; 4 is a constant term.
Combine like terms: (6m + 2m) + (-3n - n) + 4 Simplify: 8m - 4n + 4
Commentary: Remember that '-n' is the same as '-1n'. Independent Practice (Questions Only)
Simplify: 5a + 3b - 2a + b - 7 Simplify: 8x - 4y - x + 6y + 2 Solve for x: x + 3 = 10 Solve for y: y - 5 = 2 Solve for z: 4z = 20 Solve for a: a / 3 = 6 Solve for b: 2b - 3 = 7 Solve for c: c / 2 + 1 = 4 Simplify: 9p - 5q + p + 2q - 8 + 3q Solve for d: 5d + 2 = 17