Chapter 1.2, Problem 45E

(a)

To determine

To find:the solution of the equation using method one from the example three.

Answer to Problem 45E

  $x=-15$ .

Explanation of Solution

Given:

  $2\left(4-8x\right)+6=-1$ .

Concept used:

Distributive law:

In mathematics the law relating the operations of multiplication and addition, stated symbolically:

  $a\left(b+c\right)=ab+ac$ .

Here monomial factor $a$ is distributed, or separately applied, to each term of the binomial factor $\left(b+c\right)$ , resulting in the product $ab+ac$ .

Calculation:

According to the given:

  $2\left(4-8x\right)+6=-1$ .

Using distributive property and combining like terms get:

  $\begin{array}{l}2\left(4\right)+2\left(-8x\right)+6=-1.\\ 8-16x+6=-1.\\ 14-16x=-1.\\ x=-15.\end{array}$

Hence, these method gives $x=-15$ .

(b)

To determine

To find:the solution of the equation using method two from the example three and compare with first method.

Answer to Problem 45E

Method $1$ is prefer over method $2$ because it required fewer operations with fractions which makes it less complicated and reduces the chance of mistakes.

Explanation of Solution

Given:

  $2\left(4-8x\right)+6=-\frac{7}{2}$ .

Concept used:

In division method given integer $N$ and $D$ ,computes their quotient and or remainder.

Calculation:

According to the given:

  $2\left(4-8x\right)+6=-\frac{7}{2}$ .

Dividing both side by $2$ :

  $\begin{array}{l}4-8x=-\frac{7}{2}.\\ -8x=-\frac{15}{2}.\\ x=\frac{15}{16}.\end{array}$

These method gives $x=\frac{15}{16}$ .

Hence, method $1$ is prefer over method $2$ because it required fewer operations with fractions which makes it less complicated and reduces the chance of mistakes.