Questions: the sum of three and a number added to the product of two and the number is □

Transcript text: the sum of three and a number added to the product of two and the number is $\square$

Solution

Solution Steps

To translate the given phrase into a variable expression, identify the components and their relationships. "The sum of three and a number" can be written as $3 + x$. "The product of two and the number" can be written as $2x$. The entire expression is the sum of these two parts.

Step 1: Define the Variable

Let $ x $ represent "a number".

Step 2: Translate the Phrase into a Mathematical Expression

The phrase "the sum of three and a number" can be written as $ 3 + x $. The phrase "the product of two and the number" can be written as $ 2x $. The entire expression is the sum of these two parts: \[ (3 + x) + (2x) \]

Step 3: Substitute the Given Value

Given $ x = 1 $, substitute this value into the expression: \[ (3 + 1) + (2 \cdot 1) \]

Step 4: Simplify the Expression

Simplify the expression step-by-step: \[ (3 + 1) + (2 \cdot 1) = 4 + 2 = 6 \]