Algebraic Expressions and Simple Equations

An algebraic expression is a combination of numbers, variables (letters representing unknown values), and operation symbols (+, -, ×, ÷). Unlike an equation, an expression does not contain an equals sign. For example, '3x + 5' is an algebraic expression.

In an expression like '4y - 7':\n- **Variable**: A letter that represents an unknown number (e.g., 'y').\n- **Term**: Parts of an expression separated by addition or subtraction signs (e.g., '4y' and '-7').\n- **Coefficient**: The number that multiplies a variable (e.g., '4' is the coefficient of 'y').\n- **Constant**: A term that is just a number, with no variable (e.g., '-7').

Like terms are terms that have exactly the same variable part. This means they have the same variables raised to the same powers. For example, '5x' and '2x' are like terms, but '5x' and '2y' are not. '3a' and '7a' are like terms. '4' and '-9' are also like terms (constant terms).

Simplifying an algebraic expression means combining all the like terms. You can only add or subtract like terms. When combining like terms, you add or subtract their coefficients and keep the variable part the same.

An equation is a mathematical statement that shows two expressions are equal. Solving an equation means finding the value of the unknown variable that makes the equation true. To do this, we use inverse operations to isolate the variable on one side of the equals sign.

Inverse operations are operations that 'undo' each other. We use them to solve equations:\n- Addition (+) is the inverse of Subtraction (-).\n- Subtraction (-) is the inverse of Addition (+).\n- Multiplication (×) is the inverse of Division (÷).\n- Division (÷) is the inverse of Multiplication (×).

To keep an equation true and balanced, whatever operation you perform on one side of the equals sign, you must also perform the exact same operation on the other side.