Question

Simplify the expression.$x+2x+3x$

Short answer

The simplified expression is$6x$

Step-by-step solution

Step-1 – Apply the concept of terms and like terms

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property:$a(b+c)=a\cdot b+a\cdot c$

Step-2 – Use distributive property

To simplify the given expression$x+2x+3x$ , observe that all the terms are like terms as they have same variable. So, combine the terms to get the simplified expression.

Step-3 – Group and combine like terms

To simplify given expression further, group the like terms and combine them as shown below

$\begin{array}{c}x+2x+3x=(1+2+3)x\\ =(3+3)x\\ =6x\end{array}$

Thus, the simplified expression is$6x$