Chapter 12, Problem 10CLR

To determine

To Evaluate: The simplified form of the expression $3x-\left(0.4x+1.2y\right)$ .

Answer to Problem 10CLR

The value of the expression $3x-\left(0.4x+1.2y\right)$ is $2.6x-1.2y$ .

Explanation of Solution

Given information:

The expression is $3x-\left(0.4x+1.2y\right)$ .

Formula used:

The distribution laws stated as multiply a number by groups of numbers having subtraction

operation between them same as multiplication done separately. That is,

  $a(b-c-d)=ab-ac-ad$

When two terms of a expression have exactly same variable with same power is known as like term and we can perform subtraction of like terms grouping its numerical coefficients. That is,

  $ax-bx=\left(a-b\right)x$

Where $a,b$ is numerical coefficient of variable $x$ .

Calculation:

Consider the expression is $3x-\left(0.4x+1.2y\right)$ .

Recall that the distribution laws stated as multiply a number by groups of numbers having subtraction operation between them same as multiplication done separately. That is,

  $a(b-c-d)=ab-ac-ad$

Apply it,

  $\begin{array}{c}3x-1\left(0.4x+1.2y\right)=3x-1\times 0.4x-1\times 1.2y\\ =3x-0.4x-1.2y\end{array}$

Again recall that when two terms of a expression have exactly same variable with same power is known as like term and we can perform subtraction of like terms grouping its numerical coefficients. That is,

  $ax-bx=\left(a-b\right)x$

Where $a,b$ is numerical coefficient of variable $x$ .

Again use it,

  $\begin{array}{c}3x-0.4x-1.2y=\left(3-0.4\right)x-1.2y\\ =2.6x-1.2y\end{array}$

Thus, the value of the expression $3x-\left(0.4x+1.2y\right)$ is $2.6x-1.2y$ .