Question

How do you translate “twice a number \[x\]” into an algebraic expression?

Answer 1

Hint: Here, we need to write the given statement in form of an algebraic expression. An algebraic expression is a statement made by combining constants and variables using the algebraic operations of addition, multiplication, division, and subtraction. We will use the operation of multiplication to translate the given statement into an algebraic expression.

Complete step-by-step answer:
An algebraic expression can consist of different variables of different degrees and it may contain a constant but it is not necessary.
\[66 + 2x\], \[5x\], \[66{x^2} + 2x\], are all examples of algebraic expressions.
We know that twice a number is equal to the product of 2 by the number.
This means that twice the number \[x\] is equal to the product of 2 by the number \[x\].
Therefore, we get
Twice a number \[x\] \[ = 2 \times x\]
The product of a constant \[a\] and a variable \[y\] can be written without using the multiplication symbol \[ \times \]. This means that the product \[a \times y\] can be written as \[ay\].
Therefore, we can rewrite the expression \[2 \times x\] as the algebraic expression \[2x\].
Thus, we get
Twice a number \[x\] \[ = 2x\]
Therefore, we have translated “twice the number \[x\]” as the algebraic expression \[2x\].

Note: We have used the operation of multiplication to translate the given statement.
We can also use the operation of addition and distributive law of multiplication to translate it.
We know that twice a number is equal to the sum of the number with itself.
This means that twice the number \[x\] is equal to the sum of \[x\] with itself.
Therefore, we get
Twice a number \[x\] \[ = x + x\]
Rewriting the expression, we get
Twice a number \[x\] \[ = 1 \cdot x + 1 \cdot x\]
The distributive law of multiplication states that \[ba + ca = \left( {b + c} \right)a\].
Factoring the expression using the distributive law, we get
Twice a number \[x\] \[ = \left( {1 + 1} \right)x\]
Adding the terms, we get
Twice a number \[x\] \[ = 2x\]
Therefore, we have translated “twice the number \[x\]” as the algebraic expression \[2x\].