Question

How do you translate “five times the sum of a number and -3” into an algebraic expression?

Answer 1

Hint: In this problem, we need to translate the given words into an algebraic expression. Expression needs to be written using numbers and variables. Here, sum means to perform addition and times means multiplication. And also we have to let the number be ‘x’. Using these hints, we have to form an expression.

Complete step-by-step solution:
Now, let’s discuss the problem.
Before forming an algebraic expression, one should know at least these three definitions: variable, coefficient and constant. Variable is simply an alphabet whose value is unknown to us. Coefficient is nothing but a constant value which is in product with the variable. For example: In 9y, 9 is a coefficient of ‘y’. Apart from these, constant is a value which is alone in the expression and it is fixed. For example: In 4x+3, 3 is a constant term.
As per question, first we will form an expression for the sum of a number and -3. Now, you need to let a number be ‘x’ or any variable. And you have to sum it with a negative value i.e. -3. So the sum will look like:
$\Rightarrow $(x + (-3))
When we simplify using integers, it will be:
$\Rightarrow $(x -3)
So we solved half of the expression. Now, in question, it is given that we need to do 5 times the sum. For this we will multiply the sum with 5.
$\Rightarrow $5(x -3)
This is the final algebraic expression.

Note: Students usually make mistakes while doing product of 5 with the sum. They don’t consider the bracket after 5 which makes the expression as 5x -3 which is wrong. You should know the meaning of some simple words like less than means minus, added to means to add, times, product and of means to multiply.