Question

How do you solve $ 4a - 5 = 2a - 3? $

Answer 1

Hint: Move all the one side of the equation, then will simplify among the like terms and then will make the required unknown “a” the subject and find its value.

Complete step by step solution:
Take the given expression: $ 4a - 5 = 2a - 3 $
Move terms from the right hand side of the equation to the left hand side of the equation. When you move any term from one side to another then the sign of the terms also changes. Positive terms become negative and the negative term becomes positive.
 $ 4a - 5 - 2a + 3 = 0 $
Arrange the like terms together in the above equation.
 $ 4a - 2a - 5 + 3 = 0 $
Make the pair of like terms.
 $ \underline {4a - 2a} - \underline {5 + 3} = 0 $
Simplify the above expression, when you simplify between one negative and one positive term you have to perform subtraction and give sign of the bigger value to the resultant value.
 $ 2a - 2 = 0 $
Move constant on the right hand side of the equation.
 $ 2a = 2 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ a = \dfrac{2}{2} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator on the right hand side of the equation.
 $ a = 1 $
This is the required solution.
So, the correct answer is “ $ a = 1 $ ”.

Note: While simplification among the like terms remember the following rules-
I.Addition of two positive terms gives the positive term
II.Addition of one negative and positive term, you have to do subtraction and give sign of bigger numbers, whether positive or negative.
III.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.