Chapter 1.1, Problem 33E

(a)

To determine

To state: whether the inequality $-6<-10$ is true or false.

Answer to Problem 33E

  $-6<-10$ is false.

Explanation of Solution

Given information:

An inequality as $-6<-10$ .

Formula used:

For two numbers a and b

  $-a<-b$ if $a>b$

Calculation:

Consider the given inequality.

  $-6<-10$

Now, it is known that $6<10$ .

Multiply both sides by $\left(-1\right)$ .

  $\begin{array}{c}6\left(-1\right)<10\left(-1\right)\\ -6>-10\end{array}$

Hence, the inequality $-6<-10$ is false.

(b)

To determine

To state: whether the inequality $\sqrt{2}>1.41$ is true or false.

Answer to Problem 33E

  $\sqrt{2}>1.41$ is true.

Explanation of Solution

Given information:

An inequality as $\sqrt{2}>1.41$ .

Formula used:

For two numbers a and b

  $a>b$ if the digit after decimal places of a is numerically greater than digits after decimal place of b.

Calculation:

Consider the given inequality.

  $\sqrt{2}>1.41$

Now, it is known that $\sqrt{2}=\mathrm{1.414...}$ .

Now, $1.41$ can be written as $1.410$

Further 4 is numerically greater than 0.

So, $\mathrm{1.414...}>1.410$

Hence, the inequality $\sqrt{2}>1.41$ is true.