# Translate into an algebraic expression. The product of 2 and y plus the result of multiplying z...

## Question:

Translate into an algebraic expression.

{eq}\textrm{The product of 2 and } y \textrm{ plus the result of multiplying } z \textrm{ by 2 plus } x \textrm{ equals 3} {/eq}

## Algebraic Equations:

Algebraic equations are just two algebraic expressions that are equal. In order to translate sentences to algebraic equations, it is helpful to first divide the sentence into two parts based on the equality. Then write each part of the sentence as an algebraic expression individually before setting them equal.

First separate the sentences into two parts using "equals". Then break down each part of the sentence into pieces using operation words such as "plus", "product", etc. Write each part of the sentence, building it together as an algebraic expression working right to left. Finally, relate the two parts of the sentence using an equal sign.

"2 plus {eq}x {/eq}" {eq}\implies ~ 2+x {/eq}

"Multiplying {eq}z {/eq} by 2 plus {eq}x {/eq}" {eq}\implies ~ z(2+x) {/eq}

"The product of 2 and {eq}y {/eq}" {eq}\implies ~ 2y {/eq}

"The product of 2 and {eq}y {/eq} plus the result of multiplying {eq}z {/eq} by 2 plus {eq}x {/eq}" {eq}\implies ~ 2y + z(2+x) {/eq}

"The product of 2 and {eq}y {/eq} plus the result of multiplying {eq}z {/eq} by 2 plus {eq}x {/eq} equals 3" {eq}\implies ~ 2y + z(2+x) = 3 {/eq} 