Solve using Distributive Property: 3w-1-4w=4-2w (Show all work)

Question:

Solve using Distributive Property:

{eq}3w - 1 - 4w = 4 - 2w {/eq}

(Show all work)

Distributive Property:

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

Answer and Explanation:

The distributive property says that: {eq}a(b+c)=ab+ac {/eq}.

The given equation is:

$$\begin{align} 3w-1-4w&=4-2w \\[0.3cm] 3w-4w-1 &= 4-2w & [ \text{Terms are grouped} ] \\[0.3cm] w(3-4) -1 &= 4-2w & [ \text{Using distributive property in the reverse direction} ] \\[0.3cm] w(-1) -1 &= 4-2w \\[0.3cm] -w-1 &= 4-2w \\[0.3cm] w-1 &=4 & [ \text{Adding 2w on both sides} ] \\[0.3cm] w&=5 & [ \text{Adding 1 on both sides} ] \end{align} $$

Therefore, the solution of the given equation is: {eq}w= \boxed{\mathbf{5}} {/eq}.


Learn more about this topic:

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Applying the Distributive Property to Linear Equations

from Algebra I: High School

Chapter 12 / Lesson 2
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