Question

How do you solve \[12+5v=2v-9\]?

Answer 1

Hint: We will solve this question using basic linear equation concepts. First we will subtract 2v from both sides of the equation so that we get v containing terms on the LHS side. After that we will subtract 12 from the equation so that we will group the terms. After grouping by applying simple arithmetic operations we will arrive at the solution.

Complete step by step solution:
Given equation
\[12+5x=12x-10\]
First we have to group the like terms.
Group the v containing terms on one side and the remaining terms on other sides.
To group the terms we have to subtract 2v from both sides of the equation.
By subtracting 2v we will get
\[\Rightarrow 12+5v-2v=2v-2v-9\]
By simplifying above equation we get
\[\Rightarrow 12+3v=-9\]
Now we will subtract 12 from both sides of the equation.
By subtracting 12 we will get
 \[\Rightarrow 12+3v-12=-9-12\]
By simplifying we will get
\[\Rightarrow 3v=-21\]
Now to get the value of v we have to divide with 3 on both sides of the equation.
By dividing we will get
\[\Rightarrow \dfrac{3v}{3}=\dfrac{-21}{3}\]
By simplifying we will get the value of v as
\[\Rightarrow v=-7\]
So by solving the above given equation we will get \[v=-7\]

Note: We can verify the solution by back substituting the value. We will substitute -7 in the equation in place of v.
We will get
\[\Rightarrow 12+5(-7)=2(-7)-9\]
By simplifying we will get
\[\Rightarrow 12-35=-14-9\]
Now we will subtract terms on the LHS side. We will get
\[\Rightarrow -23=-14-9\]
As on the RHS side both the terms have the same sign we will add the terms.
\[\Rightarrow -23=-23\]
So we can say our equation is satisfied.