Solving Equations Vocabulary

Vocabulary terms based on the Selected Answers for Chapter 1 on Solving Equations, covering simple, multi-step, and variables on both sides.

Inverses

Operations that undo each other, specifically where $+$ and $-$ are inverses, and $\times$ and $÷$ are inverses.

Solution of an equation

A value that makes an equation true when substituted; for example, if substituting $3$ for $x$ results in the left side simplifying to $4$ and the right side to $3$, then $3$ is not a solution.

Simple Equations

Equations represented in Section 1.1 that can involve basic operations, such as $2 + 3x = 17$ where $x = 5$, or finding unknown angles like $45^∘, 45^∘, 90^∘$ by solving for $k = 45$.

Multi-Step Equations

Equations addressed in Section 1.2 that require multiple operations to solve for a variable, such as finding that $x = 13.2\text{ in.}$ or $p = -48$.

Variables on Both Sides

The topic of Section 1.3 involving equations where the unknown variable appears on both the left and right sides of the equality.

Division of Negative Numbers

A mathematical rule where a negative number divided by a negative number results in a positive number.

Substitution

The process of replacing a variable with a specific value to check if it satisfies the equation, as seen in verifying if a number is a solution.