Chapter 3.4, Problem 52PPE

(a)

To determine

To find whether the given inequality is of form $y<c$ or $y>c$

Answer to Problem 52PPE

  $y<c$

Explanation of Solution

Given:

The given inequality is $7y+2<6(4-y)$

And the given table is

Calculation:

From the given table, the inequality is true for $y\le 1.5$ and false for $y=2$ .

Therefore from the table it is clear that, the inequality is true for some real $c$ such that $y<c$ .

(b)

To determine

To estimate the value of $c$

Answer to Problem 52PPE

  $1.5$

Explanation of Solution

Given:

The given inequality is $7y+2<6(4-y)$

And the given table is

Calculation:

The inequality is true for $y\le 1.5$ i.e., the inequality is true for $y=0.5,y=1$ and $y=1.5$ is false for $y=2$ .

Then from the table, the estimated value of $c$ is $1.5$ .

(c)

To determine

To solve the given inequality.

Answer to Problem 52PPE

  $c=1.692$

Explanation of Solution

Given:

The given inequality is $7y+2<6(4-y)$

And the given table is

Calculation:

The solution of inequality $7y+2<6(4-y)$ is as follows:

  $\begin{array}{l}7y+2<6(4-y)\\ 7y+2<24-6y\\ 7y+6y<24-2\\ 13y<22\\ y<\frac{22}{13}\\ y<1.692\end{array}$

Therefore, the actual value of $c$ is $c=1.692$ and the estimated value is $c=1.5$