Question

How do you solve and check your solutions to $ 3.2 + \dfrac{x}{{2.5}} = 4.6 $ ?

Answer 1

Hint: Here first of all will move the constant term on the right hand side of the equation, and then will make the required subject “x” and simplify using the basic mathematical operations.

Complete step by step solution:
Take the given expression: $ 3.2 + \dfrac{x}{{2.5}} = 4.6 $
Move the constant term 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 \dfrac{x}{{2.5}} = 4.6 - 3.2 $
Simplify the above expression –
 $ \Rightarrow \dfrac{x}{{2.5}} = 2.3 $
Perform cross-multiplication in the above expression, where the denominator of one side is multiplied with the numerator of the opposite side.
 $ \Rightarrow x = 2.3 \times 2.5 $
Simplify the above expression, finding the product of the terms on the right hand side of the equation –
 $ \Rightarrow x = 5.75 $
This is the required solution.

Additional information: 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.

Therefore the required solution is x = 5.75.

Note: Be careful about the sign convention. Always remember that when you move any term from one side to another then the sign of the terms moving from one side to another changes. Positive terms become negative and the negative term becomes positive. Also, always remember when you multiply the decimal numbers be sure about the decimal point placed in the resultant values and the digits after the decimal point.