Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Absolute values - inequalities.
Test Yourself 1.


 

Solve each of the following inequalities and graph your result on a number line.
1. |x - 1| > 3 2. |6x - 7| > 5

3. |2m + 3| ≤ 3.

 4. |5x + 4| > 6
5. |9x + 4| ≤ 5 6.
Answer.-8 < x < 8.
7.
Answer.-5 < x < 7		 8.
Answer.x < -5 or x > 3.
9.
Answer.-5.5 < x < 0.5.		 10. (i) Sketch the graph
y = 4 - x2 indicating clearly the x and y intercepts.

(ii) On the same set of axes,
sketch y = |x| - 2

(iii) Hence or otherwise solve
4 - x2 ≥ |x| - 2.

 

11. Shade the region where the following inequalities hold simultaneously:

  • y ≥ x2 - 1
  • y ≤ x + 1