Question

How do you solve $2x + 21 = 4x + 5$?

Answer 1

Hint: Here, first all of all take the given expression and make the required term “x” the subject and move all the terms on one side of the equation and then simplify for the resultant value.

Complete step by step solution:
Take the given expression: $2x + 21 = 4x + 5$
The above equation can be re-written as –
$\Rightarrow 4x + 5 = 2x + 21$
Move constant, the term without any variable on the opposite side. When you move any term from one side to another then the sign of the term also changes. Positive terms become negative and vice-versa.
$\Rightarrow 4x - 2x = 21 - 5$
Simplify the above expression by adding the terms on right hand side of the equation –
$\Rightarrow 2x = 16$
The term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$\Rightarrow x = \dfrac{{16}}{2}$
Find the factors for the terms on the numerator.
$\Rightarrow x = \dfrac{{2 \times 8}}{2}$
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
$ \Rightarrow x = 8$
This is the required solution.

Thus the required answer is x = 8.

Note: Be careful about the sign while doing simplification and remember the golden rules-
- Addition of two positive terms gives the positive term
- Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers whether positive or negative.
- Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.