Question

How do you solve the linear equation $-5\left( 2n+3 \right)+3\left( 3n+4 \right)=-8$?

Answer 1

Hint: In the above question, we have been given an equation which is in terms of the variable n. For solving the given equation, we first need to simplify all the brackets on the LHS. For this we have to use the distributive property of the algebraic multiplication which is given by $a\left( b+c \right)=ab+ac$. Then we need to separate the variable terms on the LHS and the constant terms on the RHS. Finally, using simple algebraic manipulations, we will obtain the required value of n as the solution of the given equation.

Complete step by step solution:
The equation given to us in the above question is written as
$\Rightarrow -5\left( 2n+3 \right)+3\left( 3n+4 \right)=-8$
To solve the above equation, we have to simplify the LHS in which the numbers are being multiplied with the brackets. For simplifying we use the distributive rule of the algebraic multiplication which is given by $a\left( b+c \right)=ab+ac$. On applying this property on the LHS of the above equation, we get
\[\begin{align}
  & \Rightarrow -5\left( 2n \right)-5\left( 3 \right)+3\left( 3n \right)+3\left( 4 \right)=-8 \\
 & \Rightarrow -10n-15+9n+12=-8 \\
 & \Rightarrow -n-3=-8 \\
\end{align}\]
Multiplying the above equation by \[-1\] we get
$\Rightarrow n+3=8$
Finally, on subtracting $3$ from both the sides of the above equation, we get
$\begin{align}
  & \Rightarrow n+3-3=8-3 \\
 & \Rightarrow n=5 \\
\end{align}$
Hence, we have finally obtained the solution of the given equation as $n=5$.

Note: Do not make the mistakes of signs while applying the distributive law to simplify the LHS of the given equation. For checking any calculation mistakes, we can substitute the final obtained value of n back into the given equation and confirm whether LHS is equal to RHS.