Question

How do you solve \[-3\left( 2n-5 \right)=n+5\left( 3+7n \right)\]?

Answer 1

Hint: We will solve this question using basic linear equation concepts. First we have to remove the parentheses by multiplying with -3 on LHS and by multiplying with 5 on RHS side.

Complete step by step solution:
After removing the parenthesis we have to further simplify the equation to arrive at the solution.
Given equation
\[-3\left( 2n-5 \right)=n+5\left( 3+7n \right)\]
First we have to remove the parentheses on both sides.
Now we will remove the parentheses on the LHS side by multiplying with -3.
We will get
\[\Rightarrow -6n+15=n+5\left( 3+7n \right)\]
Now we will remove the parentheses on the RHS side by multiplying with 5.
We will get
\[\Rightarrow -6n+15=n+15+35n\]
By simplifying we will get
\[\Rightarrow -6n+15=36n+15\]
Now we have to group the like terms.
So to group the terms we have to subtract 36n on both sides of the equation.
By subtracting We will get
\[\Rightarrow -6n-36n+15=36n-36n+15\]
By simplifying we get
\[\Rightarrow -42n+15=15\]
Now we will subtract 15 on both sides of the equation.
We will get
\[\Rightarrow -42n+15-15=15-15\]
By simplification
\[\Rightarrow -42n=0\]
We already know that any number will give zero when it is multiplied with zero.
By seeing the above equation we can say that 42 is multiplied with zero inorder to satisfy the equation.
So the value of n is 0.
By solving the given equation we get the value as \[n=0\].

Note: We can also solve this by performing steps from the equation \[-42n=0\]. After this we can divide the whole equation with 42 then we will get \[-n=\dfrac{0}{42}\] . From this also we can say the value of n is zero because any number dividing zero will give 0 as quotient.