Answer – On solving 3x = 15 using the distributive property, we get x = 5.

Explanation:

Usually, an equation like $3x = 15$ can be solved in one step by dividing both sides by 3:

$3x = 15$

$÷3 ÷3$

$\Rightarrow x = 5$

This gives the solution $x = 5$.

However, since we have been asked specifically to use the distributive property, we’ll need to solve the equation using a different method to arrive at the same solution.

The distributive property can be applied to the multiplication of a term by the sum or difference of two other terms. According to this property, an expression of the form $a (b + c)$ can be solved as $ab + ac$. This also applies to an expression of the form $a (b – c)$, where the solution would $ab – ac$. Therefore, the distributive property is also often called the distributive property of multiplication over addition and subtraction.

Let’s now consider the given equation $3x = 15$.

To apply the distributive property to this equation, we need a sum or difference of two terms that can be multiplied by a common factor.

We can get such an expression by subtracting both sides of the equation by 15:

$3x – 15 = 15 – 15$

Now, we apply the distributive property:

$\Rightarrow 3 (x – 5) = 0$

We continue by simplifying the equation till we get the value of x.

Let’s divide both sides by 3 to eliminate the common factor 3:

$3 (x – 5) = 0$

$÷3 ÷3$

$\Rightarrow x – 5 = 0$

Finally, we add both sides of the equation by 5 to get the value of x:

$x – 5 = 0$

$+5 +5$

$\Rightarrow x = 5$

So the solution to $3x = 15$ using the distributive property is also found to be $x = 5$.

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