Question

How do you solve \[3\left( x-20 \right)=15\] using the distributive property?

Answer 1

Hint: This question is from the topic of algebra. For solving the equation \[3\left( x-20 \right)=15\], we will use distributive property. In solving this question, we will first disjoint the term on the left side of the equation. After that, we will take all the constant terms to the right side of the equation. After that, we will solve the further equation and find the value of x.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to solve the equation \[3\left( x-20 \right)=15\] using distributive property. We can say that we have to find the value of x from the equation \[3\left( x-20 \right)=15\]. We are going to use distributive property to solve this equation.
The equation which we have to solve is
\[3\left( x-20 \right)=15\]
Using distributive property, we can write the above equation as
\[\Rightarrow 3\times x-3\times 20=15\]
The above equation can also be written as
\[\Rightarrow 3x-3\times 20=15\]
We know that if we multiply 3 with 20, then we will get 60. So, we can write the above equation as
\[\Rightarrow 3x-60=15\]
Now, taking all the coefficients to the right side of the equation, we get
\[\Rightarrow 3x=15+60\]
The above equation can also be written as
\[\Rightarrow 3x=75\]
After dividing 3 to the both side of the equation, we get
\[\Rightarrow \dfrac{3}{3}x=\dfrac{75}{3}\]
The above equation can also be written as
\[\Rightarrow x=\dfrac{75}{3}\]
As we know that if we divide 75 by 3, we will get division as 25. So, we will write the above equation as
\[\Rightarrow x=25\]
Hence, we have solved the equation \[3\left( x-20 \right)=15\] using the distributive property and got the value of x as 25.

Note:
We should have a better knowledge in the topic of algebra to solve this type of question easily. We should know how to solve the equation using distributive property. To distribute means to divide something or give a share or part of something. The distributive property tells us that the sum of two or more addends multiplied by a number, given the same answer as distributing the multiplier, multiplying each addend separately, and adding the products together. We can write this in mathematical form as
\[a\left( b\pm c \right)=ab\pm ac\]