Solve using the distributive property: 8 y - 4 + 3 (y + 7) = 6 y - 3 (y - 3).

Question:

Solve using the distributive property: 8 y - 4 + 3 (y + 7) = 6 y - 3 (y - 3).

Distributive Property:

The distributive property is widely used while solving problems in Math. This property says to distribute multiplication over addition. It states that: {eq}a(b+c)=ab+ac {/eq}.

Answer and Explanation:

The distributive property states that:

$$a(b+c)=ab+ac $$

The given equation is:

$$\begin{align} 8 y - 4 + 3 (y + 7) &= 6 y - 3 (y - 3) \\[0.3cm] 8y-4 +3y+21 &= 6y -3y+9 & [ \text{Using the distributive property} ] \\[0.3cm] 11y+17 &= 3y+9 & [ \text{Combined the like terms} ] \\[0.3cm] 8y+17&= 9 & [ \text{Subtracted 3y from both sides} ] \\[0.3cm] 8y&=-8 & [ \text{Subtracted 17 from both sides} ] \\[0.3cm] y&=-1 & [ \text{Divided both sides by 8} ] \end{align} $$

Therefore, the solution of the given equation is: {eq}y= \boxed{\mathbf{-1}} {/eq}.


Learn more about this topic:

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Distributive Property: Definition, Use & Examples

from High School Algebra II: Help and Review

Chapter 2 / Lesson 20
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