Q9. - Algebra 1

Question

Translate each sentence into an equation. 

The sum of five times a number x and three is the same as fifteen.

Step-by-Step Solution

Answer

The required equation is $5x+3=15$.

Step 1. Apply the concept of multiplication of a constant and a variable.

A constant is a number like $1,2,10.5,$ etc. A variable is a letter or a literal used to signify an unknown quantity.

When a constant is multiplied by a variable we just append the constant in front of the variable.

We are given a constant  $5$ and a variable $x$, so their product will be  $5x$

Step 2. Apply the concept of sum for unlike terms.

Like terms are the terms having same variables and raised to the same index. Coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1. 

For example 4x and 5x are like terms.

Unlike terms are the terms not having same variables and or are raised to the different index. 

For example 4 and 5x are unlike terms.

We can add like terms by adding their coefficients, we cannot add unlike terms.

Now 5 times a number $x$ is $5x$ and we add 3 to it to obtain 

$5x+3$

Step 3. Evaluate the two results.

We have been given that the sum $5x+3$ is the same as 15 thus, we have

$5x+3=15$

Thus, the required equation is $5x+3=15$.