Hey bot, Use the Distributive Property to find the missing factors
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(1 point)
16 * __ = 3 * 7 + ( __ * 7 )
16 * 1 = 3 * 7 + ( 13 * 7 )
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Sure! Here is the step-by-step work:
16 * __ = 3 * 7 + ( __ * 7 )
To use the Distributive Property, we need to distribute the factor outside the parentheses to both terms inside:
16 * __ = 21 + ( __ * 7 )
Now, let's simplify the equation by multiplying:
16x = 21 + 7x
To isolate the variable, we can subtract 7x from both sides:
16x - 7x = 21
Simplifying further:
9x = 21
Finally, divide both sides by 9 to solve for x:
x = 21/9
Simplifying the fraction:
x = 7/3
So, the missing factors are:
16 * 7/3 = 3 * 7 + ( 7/3 * 7 )
To find the missing factors using the Distributive Property, we can rewrite the equation as:
16 * x = 3 * 7 + ( y * 7 )
Now, let's solve for the missing factors x and y step by step.
Step 1: Evaluate the expression on the right side of the equation.
3 * 7 = 21
Step 2: Simplify the expression on the right side of the equation.
21 + (y * 7) = 21 + 7y
Step 3: Rewrite the equation with the simplified expression.
16 * x = 21 + 7y
Since the missing factors are x and y, we have found the missing factors using the Distributive Property.
The missing factors are x and y, and the equation is:
16 * x = 21 + 7y
To use the distributive property, we need to distribute the factor outside the parentheses to each term inside the parentheses.
The equation is:
16 * __ = 3 * 7 + ( __ * 7 )
Let's distribute the factor 16 to each term inside the parentheses:
16 * __ = 3 * 7 + 16 * 7
Now, let's simplify each side of the equation separately:
On the left side, we have 16 times an unknown value, which we can represent as 16x:
16x = 3 * 7 + 16 * 7
The expression on the right side simplifies to:
16x = 21 + 112
Combining like terms, we have:
16x = 133
To find the value of x, we need to isolate the variable. We divide both sides of the equation by 16:
16x / 16 = 133 / 16
Simplifying further, we get:
x = 133 / 16
Therefore, the missing factor is 133/16.