Exercise 11 Page 204

We have the following compound inequality. - 4 < k+3 < 8 Let's split it into two separate inequalities. - 4 < k+3 and k+3 < 8Now we can solve them separately and later compare their solution sets.

First Inequality

We can solve inequalities just like ordinary equations. By subtracting 3 from both sides of the first inequality, we can eliminate 3 on the right-hand side. This will isolate k.

The first inequality is satisfied by all values greater than - 7. Note that k cannot equal - 7 as the inequality is strict.

Second Inequality

Now we can solve the second inequality. Again, by subtracting 3 from both sides, we can eliminate 3 on the left-hand side and isolate k.

The second inequality is true for numbers less than 5. Notice that k cannot equal 5 as the inequality is strict.

Combining Solution Sets

Finally, we can combine the obtained solution sets. The first inequality describes all values to the right of - 7, not including - 7.

The second inequality describes all values to the left of 5, not including 5.

The intersection of these sets, - 7 < k < 5, describes the solution of the compound inequality.