Chapter 1.4, Problem 13P

To determine

a.

To write:

Algebraic expression for one number in terms of another

Solution:

$16-x$.

Explanation:

1) Concept:

Here we have to use the concept of sum of two numbers.

If we have the sum of two numbers and one of the numbers is given, then the other number is difference of the total sum and the first number.

2) Given:

The sum of two numbers is 16.

And one number is $x$

3) Calculations:

If the sum of two numbers is 16 and one of the numbers is $x,$ then the expression for the other number can be written as the difference between $16$ and $x$.

Therefore, the other number is

$16-x$

Final statement:

The expression for the other number is $16-x$.

b.

To write:

Algebraic expression representing the measure of the other angle as an expression in $x$

Solution:

$180°-x$

Explanation:

1) Concept:

Two angles are supplementary if the sum of their measures is $180°.$

2) Given:

Two angles are supplementary, and the measure of one angle is $x$ degrees.

3) Calculations:

Two angles are supplementary.

So, sum of their measures is $180°$.

The measure of one angle is $x$ degrees.

Thus, the other angle can be represented as the difference of $180°$ and the measure of first angle.

That is,

$180°-x$

Final statement:

The measure of the other angle can be represented as $180°-x$

c.

To write:

An algebraic expression representing the next even integer as an expression of $x$

Solution:

$x+2$

Explanation:

1) Concept:

We have to use the relation between two consecutive even numbers: the next even integer is obtained by adding $2$ to the previous even integer.

2) Given:

$x$ is the first of two consecutive even integers.

3) Calculations:

Here, $x$ is the first of two consecutive even integers.

The next even integer can be obtained by adding $2$ to the first even integer.

Therefore, the next even integer can be obtained as $x+2.$

Final statement:

An algebraic expression representing the next even integer as an expression of $x$ is $x+2$.

d.

To write:

An algebraic expression to represent the age of the older brother as an expression of $x$.

Solution:

$x+9$

Explanation:

1) Concept:

The age of the older brother can be found by adding the number of years of difference in their ages.

2) Given:

The younger brother is $x$ years old, and the younger brother is 9 years younger than the older brother.

3) Calculations:

The younger brother is $x$ years old.

The younger brother is 9 years younger than the older brother.

That is, the difference of ages between both the brothers is $9$ years.

Therefore, the age of an older brother can be found by adding $9$ in the age of younger brother.

$Age of younger brother+difference of ages=x+9$

Thus, the age of the older brother is  $x+9$

Final statement:

An algebraic expression to represent the age of the older brother as an expression of $x$ is $x+9$.