Question

How do you write the algebraic expression given: a number $ q $ tripled plus $ z $ doubled? \[\]

Answer 1

Hint: We recall variables, constants, and algebraic expressions. We use the formation that ‘triple’ means 3 times or multiplied by 3 and ‘doubled’ means twice or multiplied by 2 times with given variables $ q,z $ to write an algebraic expression.\[\]

Complete step by step answer:
 We know that algebraic expression is a mathematical expression which consists of unknowns called variable (denoted with small letters of the English alphabet), known numbers called constants, and symbols of arithmetic operations $ \left( +,-,\times ,\div \right) $. The constants multiplied to a variable is called the coefficient of that variable, for example in $ 3x+2y+4 $ the constants are $ 3,2,4 $ , the variables are $ x,y $ and the coefficient of $ x $ is 3 and coefficient of $ y $ is 2. Each expression separated by a plus o minus sign is called a term.\[\]
We are asked in the question to write an algebraic expression for the phrase “a number $ q $ tripled plus $ z $ doubled.” So here we are given two variables $ q,z $ because we do not know their value. \[\]
We know that the word ‘triple’ means 2 times or multiplied by 3 and the word ‘doubled’ means twice or multiplied by 2 times. So we multiply $ q $ by 3 because $ q $ is tripled to have $ q\times 3=3q $ . Similarly, we multiply $ z $ by 2 because $ z $ is doubled to have $ z\times 2=2z $ .Since there is ‘plus ’ in-between ‘ $ q $ tripled’ and ‘ $ z $ doubled’ to have we add $ 3q,2z $ to have the required algebraic expression
\[3q+2z\]

Note:
We note that the obtained algebraic expression has two terms with variables $ q,z $ whose coefficients are $ 3,2 $ respectively. We must not confuse algebraic expression from numerical expression where variables do not exist and also from equations where equality signs $ ^{'}{{=}^{'}} $ always exist.