Algebra I End-of-Course (EOC)

Like terms are terms that have the same variable raised to the same power. The coefficients may differ, but the variable parts must be identical.

Examples of like terms: 3x and 7x (both have x to the first power), 5y² and -2y² (both have y squared), 4 and -9 (both are constants with no variable).

Examples of unlike terms: 3x and 3x² (different powers), 5x and 5y (different variables), 2xy and 2x (different variable combinations).

To combine like terms, add or subtract their coefficients while keeping the variable part unchanged.

When an expression contains multiple types of terms, combine each type separately.

Combine the x terms: 5x + 2x = 7x Combine the constants: 3 + 7 = 10 Result: 7x + 10

Combine y terms: 8y + 3y - y = 10y Combine constants: -4 + 12 = 8 Result: 10y + 8

Multi-step equations require more than two operations. The general strategy is to simplify each side of the equation first by combining like terms, then use inverse operations to isolate the variable.

The distributive property states that a(b + c) = ab + ac. This property is essential for eliminating parentheses in equations.

Note that when distributing a negative number, the signs of the terms inside the parentheses change.

Some equations contain multiple sets of parentheses.

Equations with fractions can be simplified by multiplying every term by the least common denominator (LCD).

The LCD of 2 and 3 is 6. Multiply every term by 6. 6(x/2) + 6(x/3) = 6(10) 3x + 2x = 60 5x = 60 x = 12

Multiplying every term by a power of 10 eliminates decimals.

A literal equation has two or more variables. Solving it for one variable uses exactly the same inverse operations — you simply treat the other letters as numbers. End-of-course exams often ask you to rearrange a formula.