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Distributive Property Test Prep AK

1. A

$\eqalign{5(y-4)&=3(y-4)\\5y-20&=3y-12\\2y-20&=-12\\2y&=8\\y&=4}$

 

2. C

$\eqalign{10x-10y&=100\\5(10x-10y)&=5(100)\\&=500}$

 

3. D

$\eqalign{a(x-y)&=81\\ax-ay&=81\\ax&=36 \quad \text {Substitute}\\36-ay&=81\\-ay&=45\\ay&=-45}$ 

 

4. 81/7

$\eqalign{(n-3)(8-15)&=-60\\(n-3)-7&=-60\\-7n+21&=-60\\-7n&=-81\\n&=\dfrac{81}{7}}$

 

5. 30  

$\eqalign{3x(4x+2)+6(4x+2)&=ax^2+bx+c\\12x^2+6x+24x+12&\\12x^2+30x+12&=ax^2+bx+c\\a&=12\\b&=30\\c&=12}$