Everything Maths Grade 11

8.2 CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES

Step 1 : Subtractx−^13 from both sides

2

x + 3

−

1

x− 3

≤ 0

Step 2 : Simplify the fraction byfinding LCD

2(x− 3)− (x + 3)

(x + 3)(x− 3)

≤ 0

x− 9

(x + 3)(x− 3)

≤ 0

Step 3 : Draw a number line for the inequality

undef undef

− (^339)

− + −^0 +

We see that the expression is negative for x <− 3 or 3 < x≤ 9.

Step 4 : Write the final answer

x <− 3 or 3 < x≤ 9

See video: VMfeu at http://www.everythingmaths.co.za

Chapter 8 End of Chapter Exercises

Solve the following inequalities and show your answer on a number line:

1. Solve: x^2 − x < 12.


2. Solve: 3 x^2 >−x + 4


3. Solve: y^2 <−y− 2


4. Solve:−t^2 + 2t >− 3


5. Solve: s^2 − 4 s >− 6


6. Solve: 0 ≥ 7 x^2 − x + 8


7. Solve: 0 ≥− 4 x^2 − x


8. Solve: 0 ≥ 6 x^2


9. Solve: 2 x^2 + x + 6≤ 0


10. Solve for x if:
    x
    x− 3
    < 2 and x�= 3.


11. Solve for x if:

4

x− 3

≤ 1.