Chapter R.17, Problem 1DE

Collect like terms.

$7x+5x$

To determine

To calculate: The simplified form of the expression $7x+5x$ by combining the like terms.

Answer to Problem 1DE

Solution:

The like terms in the expression $7x+5x$ are combined as $\underset{\_}{12x}$.

Explanation of Solution

Given information:

The provided expression is $7x+5x$.

Formula used:

For numbers a, b, and c distributive law is as below;

$a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

Consider the expression,

$7x+5x$

According to the distributive law the product of a number and a sum can be expressed as sum of two products, that is for numbers a, b, and c distributive law is as below;

$a\left(b+c\right)=a\cdot b+a\cdot c$

Use the distributive law to factor out the common variable as below:

$\begin{array}{c}7x+5x=\left(7+5\right)x\\ =12x\end{array}$

Hence, the like terms in the expression $7x+5x$ are combined as $12x$.