Hey bot, Use the Distributive Property to find the missing factors
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(1 point)
6 * __ = 3 * 7 + ( __ * 7 )
6 * 1 = 3 * 7 + ( 2 * 7 )
Show your work please
6 * 1 = 3 * 7 + ( 2 * 7 )
6 = 21 + 14
6 = 35
To use the distributive property, we need to apply the multiplication to each term in the parentheses.
The equation is:
6 * __ = 3 * 7 + ( __ * 7 )
First, let's simplify the term on the right side of the equation:
3 * 7 = 21
Now, let's distribute the multiplication to the terms in the parentheses:
6 * __ = 21 + ( __ * 7 )
Let's represent the missing factors with variables:
6 * x = 21 + ( y * 7 )
To find the missing factors, we need to isolate the variables.
Subtract 21 from both sides of the equation:
6 * x - 21 = y * 7
Now, let's rearrange the equation to isolate the y variable:
y * 7 = 6 * x - 21
To find the missing factors, divide both sides of the equation by 7:
y = (6 * x - 21) / 7
Therefore, the missing factors are represented as:
The first factor: x
The second factor: (6 * x - 21) / 7
To solve this equation using the Distributive Property, we need to distribute the 7 to both terms inside the parentheses on the right side of the equation.
Let's break down the equation step by step:
6 * __ = 3 * 7 + ( __ * 7 )
First, we simplify the multiplication on the right side:
6 * __ = 21 + ( __ * 7 )
Next, we distribute the 7 to both terms inside the parentheses:
6 * __ = 21 + 7 * __
Now, we can see that both sides have a term multiplied by an unknown factor. Let's represent the missing factors as variables:
6 * x = 21 + 7 * y
We'll now solve for the missing factors x and y to find their values.
To solve for x, we need to isolate the term with x on one side of the equation. We do this by subtracting 21 from both sides:
6 * x - 21 = 7 * y
To simplify the equation further, we divide both sides by 6:
x - 3.5 = 1.17 * y
Now, we can solve for y by isolating the term with y. We do this by subtracting 1.17y from both sides:
x - 3.5 - 1.17y = 0
At this point, we have found the missing factors x and y. The value of x is determined by the equation x - 3.5 - 1.17y = 0.