Question

How do you solve \[\dfrac{3}{2}(x-5)=-6\] ?

Answer 1

Hint:necessary calculations. After doing so, we add $\dfrac{15}{2}$ on both sides of the equation. Take LCM on the RHS of the equation and multiply it by $\dfrac{2}{3}$ as the last step to get the required solution, which is the value of x.

Complete step by step answer:
According to the question, the equation we need to solve for finding x is:
\[\dfrac{3}{2}(x-5)=-6\] --- (1)
We will start solving this problem by using Distributive property $a(b-c)=ab-ac$ on the LHS of the equation, that is
\[LHS=a(b-c)=ab-ac\]
Therefore, we get
\[LHS=\dfrac{3}{2}(x-5)=\dfrac{3}{2}x-\dfrac{3}{2}(5)\]
\[LHS=\dfrac{3}{2}(x-5)=\dfrac{3}{2}x-\dfrac{15}{2}\] --- (2)
Now, by putting the value of (2) in (1), equation (1) will become,
\[\Rightarrow \dfrac{3}{2}x-\dfrac{15}{2}=-6\]
Adding $\dfrac{15}{2}$ on both the sides of the above equation, we get
\[\Rightarrow \dfrac{3}{2}x-\dfrac{15}{2}+\dfrac{15}{2}=-6+\dfrac{15}{2}\]
As we know, the same terms with opposite signs cancel out, therefore we get
\[\dfrac{3}{2}x=-6+\dfrac{15}{2}\]
By taking LCM on RHS of the above equation, we get
$\begin{align}
  & \Rightarrow \dfrac{3}{2}x=\dfrac{-12+15}{2} \\
 & \Rightarrow \dfrac{3}{2}x=\dfrac{3}{2} \\
\end{align}$
Multiply both the sides by 2 and divide both the sides by 3 in the above equation, we get
\[\Rightarrow \dfrac{3x}{2}.\dfrac{2}{1}.\dfrac{1}{3}=\dfrac{3}{2}.\dfrac{2}{1}.\dfrac{1}{3}\]
\[\therefore x=1\]
So, for the equation \[\dfrac{3}{2}(x-5)=-6\], the value of x is equal to 1, which is our required answer.

Note:
Always mention the distributive property, while starting the solution. One of the alternative methods you can use to solve this question is first to multiply both the sides by 2 and then apply the distributive property $a(b-c)=ab-ac$. After doing so, make the necessary calculations to get the required solution to the problem, which is the value of x.
Alternate method:
Equation: \[\dfrac{3}{2}(x - 5) = - 6\]
Multiply it by 2 on both sides of the equation, we get
$\begin{align}
  & \Rightarrow \dfrac{3}{2}(x-5).(2)=-6(2) \\
 & \Rightarrow 3(x-5)=-12 \\
\end{align}$
Now, apply distributive property $a(b-c)=ab-ac$, we get
\[\Rightarrow 3x-15=-12\]
Adding 15 on both sides, we get
\[\begin{align}
  & \Rightarrow 3x-15+15=-12+15 \\
 & \Rightarrow 3x=3 \\
\end{align}\]
At last, divide both the sides by 3, that is
\[\Rightarrow \dfrac{3}{3}x=\dfrac{3}{3}\]
\[\therefore x = 1\] which is our required answer.