Question

Write an algebraic espression that models each word phrase. The product of 8 and the sum of a number x and 3

Answer 1

⇆ 8(x + 3)

Explanation:

Algebraic Expressions

Sometimes, an algebraic expression or an equation is described in words, and the task is to write it in math symbols. Or, it could be the other way round. We can have an expression in math symbols that should be written in words. But before we start, we need to familiarize ourselves with some of the important keywords that help us translate expressions.

`\hspace{370}\above7`

Common Keywords

• "increased by" indicates addition
• "decreased by" means subtraction
• "product" -> the result of multiplying 2 numbers
• "quotient" -> the result of dividing 2 numbers
• "sum" -> the result of adding 2 numbers
• "difference" -> the result of subtracting 2 numbers
• "a number" -> any letter; it's up to you which letter you choose.

`\dotfill`

The product of 8 and the sum of a number x and 3

• the sum of a number x and 3 -> x + 3
• the product of 8 and the sum -> 8(x + 3)

`\dotfill`

Answer 2

8(x + 3)

Explanation:

The first step in converting a verbal expression to an algebraic expression is determining which operation(s) will be used. The word "product" tells us multiplication will be used with the two terms or two sets of terms that follow the word, likely separated by an "and" phrase. The word "sum" tells us addition will be used with the two terms or sets of terms that follow the word, likely separated by an "and" phrase.

Now, let's identify the terms that will be multiplied together. As previously mentioned, the terms used for a product are likely separated by an "and" statement following the word "product" itself. In the verbal expression, the two terms separated by "and" are the integer 8 and the operation sum. This tell us we will be multiplying 8 by another operation. So, this gives us 8 * (the sum operation)

Next, let's identify the terms that will be added together. Just like with products, we determine this by examining which terms are separated by the "and" statement that follows the word "sum." In the verbal expression, these two terms are the variable x and the integer 3. So this gives us x + 3

Finally, we combine the two parts synthesized from the original verbal expression.

8 * (x + 3) = 8(x + 3)

The algebraic expression 8(x + 3) represents the given verbal expression.