Grade 7 Mathematics
Second Quarter
LEARNING ACTIVITY
Type of Activity: Concept Notes
Activity Title: Algebraic Expressions, Equations and Inequalities.
Learning Competency/Target:
• The learner differentiates algebraic expressions, equations, and inequalities. (M7AL-IIh-3)
• The Learner illustrates and find solution of a linear equations and inequalities in one variable
• Solves linear equation or inequality in one variable involving the absolute value, graphing and algebraic
methods.
Concept Notes:
Algebraic Expressions are expressions made up of constant and variable, along with algebraic operations
such as addition and subtraction. A variable, usually represented by a letter, takes a quantity or value that
may vary. A constant is a number, letter, or symbol whose value is fixed
Examples:
5a - 75
2y + 5y
3m – 4
An equation is a mathematical statement which expresses that two numbers or two algebraic expressions
are equal. An equation that contains a variable is an open sentence which can be true or false depending
on the value of the variable. The value of the variable that makes the equation true is a solution of the
equation.
Examples:
5m + 20 = 10
6b - 23 = 27
4p - 29 = -11
A closed sentence is a mathematical statement containing no variables.
Examples:
1+2=3
2 (6) = 12
10 - 2 = 8
An inequality is a mathematical sentence indicating that the two expressions are not equal. The
relation symbols <, <, ≤, >, ≥ 𝑎𝑛𝑑 ≠ are used to denote inequality.
Examples:
z≥7
n+9>7
k - 9 < 18
Exercises #1: Written on the cells are the examples of algebraic expressions, equation, and inequality.
Make your own examples on the blanks provided in the last row.
Algebraic Expression
𝑥+2
2𝑥 − 5
𝑥
7
Equation
2+5=7
2+x=7
X + 1 = -3
3x + 5 = 8
Inequality
c – 1 > -4
3+y≤2
2x -7 > 3 -3x
3+2≠4
Linear Equation in One Variable
A linear equation in one variable is an equation has a maximum of one variable of order 1, which is
expressed in the form ax + b = c where a and b are integers and x is a variable and has only one solution.
The symbol “=” is used to indicate equality.
Examples of a linear equations are:
x=7
3z + 4 = 12 - z
w – 3 = 10
Linear Inequality in One Variable
A linear inequality is a statement involving one variable which exponent is 1, where inequality rather than
equality is the center of focus. The word “inequality” indicates that the expression on the left and right
sides of inequality are not equal.
Exercise #2: Complete the following table by placing a check mark (✔) on the cells that illustrate linear
equation or inequality in one variable.
Equation
Inequality
1. 4x + 3 = 11
2. 7(x-2) > 12
Finding Solution of a Linear Equation from a Replacement Set
Solving an equation means finding all solutions to the equation. A solution of an equation is a
number that makes the equation a true statement. To check if a number is a solution, substitute this
number to the variable in the original equation, then perform the operations. If the substitution results in
a true statement, the number is a solution; otherwise, the solution is incorrect.
Replacement Set is a set of values that may replace a variable in an equation.
Solution Set is the set of all replacements that make an equation true.
Exercises #3:
A. Given the replacement set {−𝟐, −𝟏, 𝟎, 𝟑}, determine the solution of the given equation. Put a
check mark on the cell that corresponds to the solution then show the checking of your
solution. Put an X if the given value is not a solution. The first one is given as an example.
x+ 6=9
X=-2
X
x + 6=9
(-2)+6=9
4=9 false
X=-1
X
x + 6=9
(-1)+6=9
5=9 false
X=0
X
x+6=9
(0)+6=9
6=9 false
X=3
√
x + 6=9
3 + 6=9
9=9 true
x+2=5
A linear equation in one variable can have any of the following: exactly one solution, this equation is
called conditional equation, has infinitely many solutions or all real number is a solution for this equation,
this type of equation is called identity, and has no real solution, this type of equation is called
contradiction.
3 Different Ways to Solve an Equation or Inequality by inspection.
EXERCISES #4: Solve and graph the equation and inequality.
1. │5𝑎 − 2│ − 10 = 12
2. │𝑥 − 2│ < 5