15.11 Verbal Equation Translation

Verbal Equation Translation is the process of recognizing the words in a statement that signal an equality relationship, translating the quantities on either side of that relationship into expressions, and joining them with an equals sign to form a complete equation.

Recognizing Words That Signal Equality

Equality Phrase Identification

A verbal statement asserts an equality whenever it contains a word or phrase stating that one quantity has the same value as another, and locating this phrase is the first step in recognizing that the statement will translate into a full equation rather than a bare expression.

Is as an Equality Relation

The single word "is," when connecting two quantities in a statement, signals an equals sign in the symbolic translation, functioning as the simplest and most common equality phrase.

Is Equal to as an Equality Relation

The phrase "is equal to" functions identically to the single word "is," signaling an equals sign between the quantity described before it and the quantity described after it.

Equals as an Equality Relation

The word "equals," used directly between two quantities, also signals an equals sign in the translation, functioning the same way as "is" or "is equal to" despite the slightly different grammatical construction.

Results in as an Equality Relation

The phrase "results in," often used when describing the outcome of a calculation or process, signals an equals sign between the described process and its stated outcome.

Translating Each Side

Left-Side Quantity Translation

The portion of the verbal statement appearing before the identified equality phrase is translated into its own expression, following all the same rules used for translating any expression, and becomes the left side of the resulting equation.

Right-Side Quantity Translation

The portion of the verbal statement appearing after the identified equality phrase is translated into its own separate expression, becoming the right side of the resulting equation.

Assembling the Equation

Simple Verbal Equation Construction

A statement with a single operation on each side of the equality phrase translates directly into an equation with a simple expression on each side, joined by an equals sign in place of the identified equality phrase.

Grouped Expression Equation Construction

A statement describing a grouped sum or difference on either side of the equality phrase requires that grouping to be preserved with parentheses in the translated equation, exactly as it would be within an ordinary expression.

Multivariable Verbal Equation Construction

A statement involving more than one unknown quantity translates into an equation containing more than one variable, with each variable assigned according to the same identification process used for any multivariable translation, and both sides of the equation built from whichever variables the statement actually describes.

What Comes After Translation

Equation Construction without Solving

Translating a verbal statement into an equation produces only the equation itself; determining the specific value of the variable that makes the equation true is a separate task of solving that follows translation rather than being part of it.

Flexibility in Writing the Equation

Equality Direction and Equivalent Reversal

Because an equation states that two quantities are equal, writing the translated equation with its two sides reversed, so that what was the right side becomes the left side and vice versa, produces an equally valid and equivalent equation, since equality holds in both directions.