Question

How do you solve $7x - 2 = 3x + 18?$

Answer 1

Hint: According to the question we have to solve the expression which is as given in the question $7x - 2 = 3x + 18$. So, first of all to determine the value of x we have to use the elimination method but before that we have to understand about the elimination method which is as explained below:
Elimination method: According to elimination method we just have to eliminate the terms of the expression but before that we have to make the given variables same for both of the expressions given which can be done by multiplying or dividing the terms in the given variable to make them as a same term or variable. Then we have to subtract the terms of the expressions so that we can determine the value of any one of the variables.
First of all we have to take all the variables in any one side of the expression means we can take the given variable to the right hand side or to the left hand side.
Now, we have to add or subtract the terms which can be subtracted or added and in the expression obtained after taking the variable in the same side.

Complete step-by-step solution:
Step 1: First of all we have to take all the variables in any one side of the expression means we can take the given variable to the right hand side or to the left hand side as mentioned in the solution hint. Hence,
$ \Rightarrow 7x - 3x = 18 + 2...............(1)$
Step 2: Now, we have to add or subtract the terms which can be subtracted or added and in the expression (1) obtained after taking the variable in the same side which is as mentioned in the solution hint. Hence,
$ \Rightarrow 4x = 20$……………(2)
Step 3: Now, to solve the expression which is as obtained in the solution step 2 we have to apply the cross-multiplication in the expression obtained to determine the value of x. Hence,
$
   \Rightarrow x = \dfrac{{20}}{4} \\
   \Rightarrow x = 5
$

Hence, with the help of the elimination method we have determined the solution of the given expression $7x - 2 = 3x + 18$ which is $ x = 5$.

Note: To determine the value of the variable x which is as given in the question it is necessary that we have to take both of the variables in the same side of the expression and then we have to solve the expression obtained by eliminating the terms or variables.
To eliminate the terms of the expression but before that we have to make the given variables same for both of the expressions given which can be done by multiplying or dividing the terms in the given variable to make them as a same term or variable.