Write the corresponding algebraic expression or equation for the verbal state 2 less than four times the sum of a number and 3
The correct answer and explanation is:
The correct algebraic expression for the verbal statement “2 less than four times the sum of a number and 3” is: 4(x+3)−24(x + 3) – 2
Explanation:
Let’s break down the expression step by step.
- “a number”: This represents an unknown value, which we typically denote with a variable, such as xx. So, “a number” is represented by xx.
- “the sum of a number and 3”: The sum of the unknown number and 3 is written as x+3x + 3. This indicates that we are adding 3 to the variable xx.
- “four times the sum”: This means multiplying the sum x+3x + 3 by 4. The multiplication operation is represented as 4(x+3)4(x + 3).
- “2 less than”: This indicates subtraction, meaning we are subtracting 2 from the expression 4(x+3)4(x + 3). The phrase “2 less than” corresponds to 4(x+3)−24(x + 3) – 2.
Thus, the complete algebraic expression for the verbal statement is: 4(x+3)−24(x + 3) – 2
Final Thoughts:
This algebraic expression correctly translates the words into mathematical terms by following the order of operations. The parentheses around x+3x + 3 are important because they indicate that the addition should happen before the multiplication by 4. After the multiplication is done, the 2 is subtracted to complete the expression.