Question

How do you solve 3x + 5 = 2x + 7?

Answer 1

Hint: To solve this linear equation in two variables we will first transpose the term 2x from RHS to LHS. Similarly we will transpose 5 to RHS. Now we will simplify the equation by subtracting the terms obtained on LHS and RHS. Hence we will get the solution to the given equation.

Complete step-by-step solution:
We are given with a Mathematical equation which is a linear equation in one variable.
Let us first understand what a linear equation is.
Linear equations are the equations in which the highest power of a variable is 1.
Which means there are no terms of the form \[{{x}^{2}},{{x}^{3}}\] or \[{{x}^{n}}\] .
Now if there is just one variable in the equation we call it a linear equation in one variable.
Now Linear equation in one variable are the equations which can be written in the form
ax + b = 0. Where a and b are integers and x is the variable.
Now to solve any linear equation we will first transpose all the variables on one side and integers on the other side. Now we will simplify the equation to find the value of x
Now consider the given equation 3x + 5 = 2x + 7.
Now let us transpose 2x from RHS to LHS. Hence 2x will be – 2x when it comes to LHS.
Hence, we get 3x – 2x + 5 = 7.
Now similarly let us transpose 5 to RHS.
Hence, we get 3x – 2x = 7 – 5.
Now solving this equation we get x = 2.
Hence the solution of the equation is x = 2.

Note: Now first note that when we transpose a term from one side to another the sign of the term changes. Hence + 2x becomes – 2x and + 5 becomes – 5 when taken to the other side. Also always remember to check the answer by substituting the answer in the given equation.