Chapter 2 Reasoning and Proof

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• Skills Handbook, p. 830 Evaluating Expressions

  Algebra Evaluate each expression for the given value of x.

  1. 9 x − 13  for  x = 7 9 x minus 13 , for , x equals 7
  2. 90 − 3 x  for  x = 31 90 minus 3 x , for , x equals 31
  3. 1 2 x + 14  for  x = 23 1 half , x plus 14 , for , x equals 23

• Skills Handbook, p. 834 Solving Equations

  Algebra Solve each equation.

  4. 2 x − 17 = 4 2 x minus 17 equals 4
  5. 3 x + 8 = 53 3 x plus 8 equals 53
  6. ( 10 x + 5 ) + ( 6 x − 1 ) = 180 open 10 x plus 5 close plus open 6 x minus 1 close equals 180
  7. 14 x = 2 ( 5 x + 14 ) 14 x equals 2 open 5 x plus 14 close
  8. 2 ( x + 4 ) = x + 13 2 open x plus 4 close equals x plus 13
  9. 7 x + 5 = 5 x + 17 7 x plus 5 equals 5 x plus 17
  10. ( x + 21 ) + ( 2 x + 9 ) = 90 open x plus 21 close plus open 2 x plus 9 close equals 90
  11. 2 ( 3 x − 4 ) + ( 10 ) = 5 ( x + 4 ) 2 open 3 x minus 4 close plus open 10 close equals 5 open x plus 4 close

• Lessons 1-3 through 1-5 Segments and Angles

  Use the figure below.

  

  12. Name ∠ 1 angle 1  in two other ways.
  13. If D is the midpoint of A B ¯ , eh b bar , comma  find the value of x.
  14. If ∠ A B C angle eh b c  is a right angle, m ∠ 1 = 4 y , m angle 1 equals 4 y comma  and m ∠ 2 = 2 y + 18 , m angle 2 equals 2 y plus 18 comma  find m ∠ 1 m angle 1  and m ∠ 2 . m angle 2 .
  15. Name a pair of angles that form a linear pair.
  16. Name a pair of adjacent angles that are not supplementary.
  17. If m ∠ A D C + m ∠ B D C = 180 , m angle eh d c plus m angle b d c equals 180 comma  name the straight angle.

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