Expanding Algebraic Expressions and Solving Linear Equations

Vocabulary flashcards covering topics on expanding brackets using the distributive law, simplifying algebraic expressions, and solving linear equations.

Distributive Law

A rule used to expand and remove brackets by multiplying the term on the outside of the brackets by each term inside the brackets, expressed as $a(b + c) = ab + ac$.

Pronumerals

Symbols or variables used in algebraic expressions to represent numbers.

Expansion with a Negative Multiplier

The expansion process when the number in front of a bracket is negative, which changes the sign of each term inside the brackets (for example, $-2(x - 3) = -2x + 6$).

Edge Squares Formula for Dance Floors

The algebraic expression $2x + 2(y - 2)$ used to calculate the total number of $1\,\text{m}$ by $1\,\text{m}$ edge squares for a portable dance floor measuring $x\,\text{m}$ by $y\,\text{m}$.

Inner Squares Formula for Dance Floors

The algebraic expression $(x - 2)(y - 2)$ used to calculate the total number of $1\,\text{m}$ by $1\,\text{m}$ inner squares for a portable dance floor measuring $x\,\text{m}$ by $y\,\text{m}$.

Negated Bracket Expansion

An expansion where a minus sign in front of a bracket acts as a multiplier of $-1$, such that $-(3x + y) = -1(3x + y) = -3x - y$.

Equation

A mathematical statement containing an equals sign, a left-hand side, and a right-hand side.

Linear Equation

An equation that can be written in the form $ax + b = c$, where the power of the variable $x$ is $1$.

Solving an Equation

The process of finding the value of a variable or pronumeral that makes the mathematical equation true.

Inspection Method

A method used to solve simple linear equations by mental observation, such as determining $x = 5$ for $3x = 15$.

Equivalent Equations

Equations that share the exact same solution, created by adding, subtracting, multiplying, or dividing both sides by the same non-zero number.

Inverse Operations (Backtracking)

The procedure of creating equivalent equations by applying opposite mathematical operations to both sides step-by-step to isolate a variable.

Solution Checking

The verification process of substituting a calculated value back into the original equation to confirm that the left-hand side equals the right-hand side.

Guess and Check (Trial and Error)

A technique used to find the solution to an equation by testing values for the variable without writing out intermediate steps.