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

Algebra - Absolute values - linear equations.
Test Yourself 1.


 

Solve each of the following equations.
1 term in x. 1. |t| = 42
Answer.t = + 42 or t = -42.		 2. |6t| = 24
Answer.t = + 4 or t = -4.
  3. |3x + 2| = 8
Answer.x = 2 or x = -10/3.		 4. |3 - 2x| = 5
Answer.x = -1 or x = 4.
  5. |-2x - 3| = 7
Answer.x = -5 or x = 2.		 6.
  7. 8.
  9. |x2 - 3| = 6
Answer.x = 3 or x = -3.		 10. |x2 + 3| = 8
Answer.x = √5 or x = -√5.
2 terms in x

Careful - need to check your answers now.
For the simpler questions, a graph would also help.

11. |2x + 3| = 3x
Answer.x = 3 or x = -0.6.		 12. |3x + 1| = 2x + 4
Answer.x = √19 or x = -√19.
13. |4 - 2x| = x - 2
Answer.Only x = 2.		 14. |2x + 5| = 3x + 9
Answer.x = -2.8 NOT x = -4.
15. |x - 2| - x = 1
Answer.x = 0.5.		 16. |2x + 6| = |x + 10|
Answer.x = 4 or -16/3.
17. 2|x + 8| = 3 |x + 5|
Answer.x = -2.8 NOT x = -4.		 18. |6x - 7| = 2|4 - 2x|
Answer.x = 1.5 or x = -0.5.
  19. 6|x + 3| - 2|x + 1| = 0
Answer.x = -4 or x = -2.5.		 20.
  21.
Answer.x = -27/4 (or -6.75) and -10.5.		 22.
Answer.x = +2 or -2.
  23. |x2 - 21| = 4x
Answer.x = +3 or +7 but NOT -3 or -7.		 24. |x2 + x| = x2 - 3
Answer.x = -3 but NOT -1.5 or 1.
  25. (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.

 26.