Question

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

Answer 1

Hint: Now the given equation is a linear equation in v. To solve the equation we will group all the terms with variables and separate the terms from constants. To do so we will transpose 2v to LHS and 12 to RHS. Now we will simplify the equation and divide the equation by the coefficient of v and hence find the value of v.

Complete step by step solution:
We are given with a linear equation in one variable v, \[12+5v=2v-9\]
Now to solve the equation means to find the value of v for which the equation holds.
First we will separate the constant terms and variable terms.
Hence we will transpose 2v on LHS and 12 on RHS. Hence we get,
$\Rightarrow 5v-2v=-12-9$
Now we know that we can add and subtract the terms with the same variable and same degree. Hence we get $\Rightarrow 3v=-21$
Now dividing the whole equation by coefficient of v which in this case is 3 we get,
$\Rightarrow v=\dfrac{-21}{3}=-7$
Hence the value of v is – 7.

Note:
Now note that while transposing any term from one side to another the sign of the term changes. Hence in the above example + 12 changes to – 12 when taken to RHS and 2v changes to – 2v when taken to LHS. Similarly multiplication changes to division and division changes to multiplication while transposing to the other side. Also always check the solution of the linear equation by substituting the value of x in the equation. Hence if the solution is correct the equation will hold true.