Page 5 - Algebra

1.2. Algebraic Equation
An algebraic equation is a mathematical expression with two expressions equal to each other. The algebraic equation of the above example,
4x – 7 = 1 or
4x – 7 = 5
The statement on the left-hand side equals the statement on the right-hand side. A basic difference between an algebraic expression and algebraic equation it the ‘=’ operator.
Worked Example
Which of the following are an algebraic expression and algebraic equation?
a. 5y + 8
b. 7z – 10 = 4
c. x + 2 = 5
Solution:
a. It’s an algebraic expression because ‘=’ operator is absent.
b. It’s an algebraic equation because it has a ‘=’ operator.
c. It’s an algebraic equation because it has a ‘=’ operator.
1.3. Solving Algebraic Expression
Adding and Subtracting Algebraic Expressions
When adding or subtracting an algebraic expression, you have to combine the like terms.
• Like terms
Like terms are terms with the same variable and the same exponent. It’s similar to adding oranges with oranges and not apples.
Worked Example
Find the sum of the following algebraic expression:
(5x – 12) + (4x + 3)
Solution:
Write the term without parenthesis
5x – 12 + 4x + 3
Combine the like terms. Here the like terms are constants and variables. The variables are 5x and 4x,
and the constants are – 12, and 3.
5x + 4x – 12 + 3
Now, add the like terms
9x – 9
REMEMBER:
When subtracting two algebraic expressions, distribute
distributing –1, change the sign of each term.
–1 in the second parenthesis. When
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Algebra I & II