Question

How do you simplify \[3(4 + 5s) - 12 + ( - 3s)\] ?

Answer 1

Hint: Here in this question, we have to simplify the equation for only terms that is s. The equation involves one variable “s” by using the arithmetic operations to equation we have to find the equation for the variable “s”. hence we get the equation.

Complete step-by-step answer:
The given equation or expression is an algebraic expression, where it is a combination of both variables and constants where variables are alphabets and the constants are numbers. The given equation is a binomial equation. The binomial equation is an algebraic expression which contains the terms and the arithmetic operations that are addition and subtraction.
Here in this question, we should know about the sign conventions.
The sign conventions for addition operation is given as
 \[( + )\,\, + \,\,( + )\,\, = \,\,addition\]
 \[( + )\,\, + \,\,( - )\,\, = \,\,subtraction\]
 \[( - )\,\, + \,\,( - )\,\, = \,\,addition\]
Here which operation should be done to the terms will be defined.
The sign conventions for multiplication operation is given as
 \[( + )\,\, \times \,\,( + )\,\, = \,\, + \]
 \[( + )\,\, \times \,\,( - )\,\, = \, - \]
 \[( - )\,\, \times \,\,( - )\,\, = \,\, + \]
Here which sign does the term should have, will defines
Now consider the given expression
 \[3(4 + 5s) - 12 + ( - 3s)\]
In the first term we multiply the term and hence we apply sign conventions and we get
 \[ \Rightarrow 12 + 15s - 12 - 3s\]
The 12 and -12 will get cancelled.
 \[ \Rightarrow 15s - 3s\]
The both terms has same variable, on subtracting we get
 \[ \Rightarrow 12s\]
Hence the binomial expression has simplified to the monomial expression.
Hence we have simplified the given algebraic expression.
So, the correct answer is “12s”.

Note: The equation is differ from expression. In the equation the algebraic expression is equated to some numeral or zero. the expression is an inequality which is not equated to some numeral or zero. The mathematical operation is applied to the like terms or same variable.