Question

How do you solve $3x-5=2.5x+3-\left( x-4 \right)$ ?

Answer 1

Hint: We are given a one-degree polynomial equation in x-variable which has multiple terms of x-variable and multiple constant terms. Firstly, we shall open the brackets on the right-hand side. Then, we will transpose all the constant terms on the right hand side and perform simple addition or subtraction according to the equation. Further, we will make the coefficient of x equal to 1 to obtain our final solution of the given equation.

Complete step by step solution:
Given that $3x-5=2.5x+3-\left( x-4 \right)$.
Opening the brackets with the negative sign on the right-hand side, we get
$\Rightarrow 3x-5=2.5x+3-x+4$
There are two constant terms and two terms of variable-x on the right hand side and one term of x-variable and one constant term on the left hand side.
We shall transpose the constant on the left hand side of the equation to the right hand side. Then we will transpose the two terms of x-variable on the right hand side of the equation to the left hand side.
$\Rightarrow 3x-2.5x+x=3+4+5$
Performing simple addition and subtraction, we get
$\Rightarrow 1.5x=12$
Dividing both sides by 1.5, we get
$\Rightarrow x=\dfrac{12}{1.5}$
$\Rightarrow x=8$
The solution of the equation is the value of the variable-x which will be obtained on solving the equation and we have calculated variable x equal to 8.

Therefore, the solution of the given equation $3x-5=2.5x+3-\left( x-4 \right)$ is $x=8$.

Note: While transposing any term from the left hand side to the right hand side or vice-versa in an equation, the sign of the term is reversed. One possible mistake we could have made was that we might forget to change the sign of the term which was being transposed in the equation.