Algebra Class 9: Order of Operations and One-Variable Equations

Study Notes

There is a specific order of operations to follow when working with algebraic expressions.

The equation 2x + 5 = 11 has no solution, indicating that there is no value of x that satisfies the equation.
To solve for x in the equation 3x - 2 = 14, we can add 2 to both sides, resulting in 3x = 16, and then divide both sides by 3 to get x = 16/3.

To solve the inequality 2x - 3 > 5, we can add 3 to both sides of the inequality to get 2x > 8, and then divide both sides by 2 to get x > 4.

This section requires matching equations with their corresponding solutions, but no specific equations or solutions are provided.

Algebra involves the use of variables, constants, and mathematical operations to solve equations and inequalities.
Variables are letters or symbols that represent unknown values or quantities.
Constants are numbers or values that do not change.

The order of operations is a set of rules used to evaluate expressions containing multiple operations.
The acronym PEMDAS is commonly used to remember the order:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate from left to right.
- Addition and Subtraction: Evaluate from left to right.

A one-variable equation is an equation that contains one variable.
The goal of solving an equation is to isolate the variable on one side of the equation.
Equations can be solved using inverse operations:
- Addition and subtraction: Use opposite operations to isolate the variable.
- Multiplication and division: Use opposite operations to isolate the variable.
Equations with variables on one side can be solved by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

A one-variable inequality is an inequality that contains one variable.
Inequalities can be solved using similar methods as equations, but with some differences:
- When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed.
Inequalities can be written in different forms, including:
- Less than: <
- Greater than: >
- Less than or equal to: ≤
- Greater than or equal to: ≥

Equations and inequalities can have variables on both sides.
To solve, use the same methods as above, but combine like terms on each side of the equation or inequality before isolating the variable.
Simplify the equation or inequality by combining like terms and using inverse operations to isolate the variable.