Exercise 10 Page 210

To solve the quadratic inequality algebraically, we will follow three steps.

1. Solve the related quadratic equation.
2. Plot the solutions on a number line.
3. Test a value from each interval to see if it satisfies the original inequality.

Step 1

We will start by solving the related equation. x^2-14x=- 49 ⇔ 1x^2+( - 14)x+ 49=0We see above that a= 1, b= - 14, and c= 49. Let's substitute these values into the Quadratic Formula to solve the equation.

The root of the equation is 7

Step 2

The solution of the related equation is 7. Let's plot it on a number line. Since the original is a strict inequality, the point will be open.

Step 3

Finally, we must test a value from each interval to see if it satisfies the original inequality. Let's choose a value from the first interval, x < 7. For simplicity, we will choose x=0.

Since x=0 produced a true statement, the interval x < 7 is a part of the solution. Similarly, we can test the other interval.

We can now write the solution set and show it on a number line. {x|x≠ 7} or (- ∞ , 7) ⋃ (7, + ∞)