Question

How do you translate the following statement “Five less than a number is seventeen” into an algebraic expression and then find the number?

Answer 1

Hint: We know that mathematical expression and algebraic expression are both the same. An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. We know that if we have ‘less than’ we use the operation we use subtraction signs.

Complete step-by-step solution:
We have “five less than a number is seventeen”.
Let the unknown number be ‘x’.
Then five less than a number means \[ \Rightarrow x - 5\]
Then we have “five less than a number is seventeen”.
\[ \Rightarrow x - 5 = 17\]is the required algebraic expression.
Because we have a constant ‘5’, ‘17’ and a variable ‘x’. Also we have algebraic operation subtraction.
Now to find the number.
\[ \Rightarrow x - 5 = 17\]
Adding 5 on both side we have
\[ \Rightarrow x = 17 + 5\]
\[ \Rightarrow x = 22\]

Hence the equation is x - 5 = 17 and the value of x is 22

Note: A variable is a symbol for a number that we don’t know yet. Generally it is represented by alphabetic letters. A number on its own is called a constant. Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation \[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have a ‘quotient’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.