Six times the sum of a number and four
The Correct Answer and Explanation is :
Let’s go through the math first.
Let the unknown number be represented by ( x ).
According to the question:
Six times the sum of a number and four
This means we add four to the number ( x ), and then multiply the sum by six. So, we can represent this algebraically as:
[
6 \times (x + 4)
]
To simplify, we distribute the 6 across the terms inside the parentheses:
[
6 \times (x + 4) = 6x + 24
]
Explanation of the Steps
- Understanding “the sum of a number and four”: When we say “the sum of a number and four,” we mean that we are adding 4 to the unknown number, ( x ). In algebra, this sum can be written as ( x + 4 ). The parentheses around ( x + 4 ) are crucial because they group these terms together, indicating that we should perform operations on this entire quantity.
- Multiplying the Sum by Six: The phrase “six times the sum” indicates that we should multiply the entire expression ( x + 4 ) by six. This multiplication is written as ( 6 \times (x + 4) ).
- Distributing the Six: To simplify, we use the distributive property, which tells us that ( a(b + c) = ab + ac ). Applying this to our expression, we get:
[
6 \times (x + 4) = 6x + 24
] - Result: After simplifying, the expression ( 6(x + 4) ) becomes ( 6x + 24 ). This is the final, simplified answer.
This expression can now be used in an equation if we’re solving for ( x ) or as part of a larger problem. In general, understanding how to translate words into algebraic expressions and then simplify is a key skill in math, as it allows us to work with unknown quantities and find solutions in a structured, logical way.