Question

How do you write the phrase as an expression, then evaluate when \[x = 5\]: \[6\] more than the product of \[8\] and a number \[x\]?

Answer 1

Hint: Here, we will use the keyword of the phrase to write the expression in parts. We will then combine each part to form the required algebraic expression. We will then substitute the value of the variable in the obtained expression and simplify it further to get the required answer.

Complete Step by Step Solution:
We are given an algebraic expression \[x = 5\] such that \[6\] more than the product of \[8\] and a number \[x\].
We are given that the unknown number is represented in the form of variable as \[x\].
We know that the product represents the arithmetic operation of multiplication.
So, the product of \[8\] and a number \[x\] can be represented as \[8 \times x\] or \[8x\].
We know that the keyword more than represents the arithmetic operation of addition.
So, \[6\] more than the product of \[8\] and a number \[x\] can be represented as \[8x + 6\].
Now, we will evaluate the algebraic expression by substituting \[x = 5\], we get
\[8x + 6 = 8\left( 5 \right) + 6\]
Multiplying the terms, we get
\[ \Rightarrow 8x + 6 = 40 + 6\]
Adding the terms, we get
\[ \Rightarrow 8x + 6 = 46\]

Therefore, the algebraic expression for the phrase \[6\] more than the product of \[8\] and a number \[x\] is \[8x + 6\] and the value when \[x = 5\] is \[46\].

Note:
We know that Arithmetic expression or Mathematical expression is defined as an expression with the numbers and the arithmetic operators like plus, minus etc whereas Algebraic expression is defined as an expression with both the numbers and the variables and the arithmetic operators like plus, minus, etc. We have many ways to represent an algebraic expression into the word phrase. Word phrase is a way of representing the algebraic expression or mathematical expression in the form of sentences using the keywords. We should know that there is no single strategy for converting an algebraic expression into a word phrase and vice versa. We should remember that after writing the algebraic expression, we should evaluate for the given value of the variable.