Question

___________ shows “five more than twice a number.” $$ \begin{array}{|l|l|} \hline \text { Select... } & \nabla \\ \hline 5+2 x & \\ \hline 5 x+2 \\ \hline 5+2+x & \\ \hline \end{array} $$

Short answer

5 + 2x

Step-by-step solution

Understand the Phrase

The phrase 'five more than twice a number' means we need to find the expression where we start with twice a number and then add five to it.

Identify 'Twice a Number'

Let 'a number' be represented by the variable 'x'. 'Twice a number' can be mathematically written as '2x'.

Add Five

According to the phrase, we need to add five to the expression '2x'. Therefore, the expression becomes '2x + 5'.

Match the Expression

Look at the options provided and match the expression we derived: '5 + 2x'. This is the same as '2x + 5' because addition is commutative.

Key concepts

mathematical phrases

When learning algebra, understanding mathematical phrases is essential. A mathematical phrase describes an operation that needs to be performed. In this case, the phrase is 'five more than twice a number'.
This tells us to start with doubling a number, then adding five to the result.
Breaking down phrases helps in translating them into algebraic expressions accurately. If you encounter phrases like 'more than', 'less than', or 'times', think about the mathematical operation that corresponds to the phrase.
It is important to understand each word in the phrase to properly form an algebraic equation.
Recognizing and properly translating these phrases enables better comprehension and problem-solving skills in algebra.

variable representation

In algebra, variables are symbols used to represent unknown values. Usually, we use letters such as 'x' or 'y'.
For the phrase 'twice a number', we need to represent 'a number' with a variable. Let's use 'x' here.
'Twice a number' means multiplying that variable by 2, so it becomes '2x'.
Understanding variable representation is key in simplifying and solving algebraic expressions.
Make sure you recognize how variables can stand in for actual numbers, making it easier to perform operations and solve equations.
Practice identifying and using variable representations in different mathematical contexts to gain confidence.

commutative property of addition

The commutative property of addition states that the order in which you add numbers does not change the sum. In other words, \(a + b = b + a\).
For example, if we have '2x + 5', it is the same as '5 + 2x'.
In our exercise, after forming the expression '2x + 5', we can match it to the provided option '5 + 2x' because of the commutative property.
This property simplifies algebraic operations, ensuring that any rearrangement of terms when adding does not affect the result.
Always remember that understanding this property helps in rearranging and simplifying expressions correctly, making complex problems simpler to solve.