Question

How do you solve $3x+8=5x-20$?

Answer 1

Hint: The given equation is a linear equation in one variable. To solve the equation first we will shift the terms with variables at the LHS and constant terms at the RHS. Then by solving algebraic operations we get the desired answer.

Complete step-by-step solution:
We have been given an equation $3x+8=5x-20$
We have to solve the given equation and find the value of the unknown variable x.
As the given equation is a linear equation in one variable. Linear equation in one variable is an equation which has only one unknown variable and also the variable has only one solution. In the given equation x is an unknown variable and we have to find the value of x.
Now, to solve the given equation first we rearrange the terms of the equation and rewrite as
$\Rightarrow 3x-5x=-20-8$
Now, simplifying the above obtained equation we will get
$\Rightarrow -2x=-28$
Now, let us divide the above obtained equation by $-2$. Then we will get
\[\Rightarrow \dfrac{-2x}{-2}=\dfrac{-28}{-2}\]
Now, simplifying the above obtained equation we will get
$\Rightarrow x=14$
Hence on solving the given equation $3x+8=5x-20$ we get the value $x=14$.

Note: Be careful while shifting the terms, the signs get reversed when we shift the terms from LHS to RHS or vice-versa. Here in the given equation only one variable is unknown so we can find the value by solving the algebraic operations given in the equation. We can also verify the obtained answer by putting the value of the variable in the given equation.