What’s the answer 7x + 7=7(x+_)
The Correct Answer and Explanation is :
To solve the equation ( 7x + 7 = 7(x + __) ), we need to determine the value that should replace the blank space (__).
Step 1: Simplify the right side of the equation
The equation can be rewritten as follows:
[
7x + 7 = 7(x + __)
]
We can distribute the (7) on the right side:
[
7x + 7 = 7x + 7 \cdot __
]
Step 2: Set the left side equal to the right side
Since both sides have (7x), we can simplify further by subtracting (7x) from both sides:
[
7 = 7 \cdot __
]
Step 3: Solve for the blank space (__)
To isolate the blank, we can divide both sides of the equation by (7):
[
\frac{7}{7} = __
]
This simplifies to:
[
1 = __
]
Thus, the correct value that replaces the blank is (1).
Conclusion
The completed equation is:
[
7x + 7 = 7(x + 1)
]
This equation illustrates the distributive property of multiplication over addition. In essence, the left side ((7x + 7)) can be expressed as (7) multiplied by the sum of (x) and (1) on the right side ((7(x + 1))). This relationship shows that adding a constant to the variable can be factored out when multiplied by a coefficient (in this case, (7)).
Understanding this principle is essential in algebra as it helps to simplify and solve equations more efficiently. It highlights how expressions can be manipulated while maintaining equality, which is a foundational concept in mathematics.