Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through Explorations 1 and 2, and Communicate Your Answer on page 11. Remember you are solving a problem situation by setting up an equation and then solving for the variable. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 11)

1. (30 + x) + 9x + 30 = 180; Write the equation.
   10x + 60 = 180; Combine like terms.
   10x = 120; Subtract 60 from each side.
   x = 12; Divide each side by 10.
   42°, 108°, 30°
2. (x + 10) + (x + 20) + 50 = 180; Write the equation.
   2x + 80 = 180; Combine like terms.
   2x = 100; Subtract 80 from each side.
   x = 50; Divide each side by 2.
   60°, 70°, 50°
3. 50 + (2x + 30) + (2x + 20) + x = 360; Write the equation.
   5x + 100 = 360; Combine like terms.
   5x = 260; Subtract 100 from each side.
   x = 52; Divide each side by 5.
   50°, 134°, 124°, 52°
4. (x – 17) + x + (x + 42) + (x + 35) = 360; Write the equation.
   4x + 60 = 360; Combine like terms.
   4x = 300; Subtract 60 from each side.
   x = 75; Divide each side by 4.
   58°, 75°, 117°, 110°
5. (5x + 2) + (3x + 5)+ (8x + 8) + (4x + 15) + (5x + 10) = 540; Write the equation.
   25x + 40 = 540; Combine like terms.
   25x = 500; Subtract 40 from each side.
   x = 20; Divide each side by 25.
   102°, 65°, 168°, 95°, 110°
6. (3x + 16) + (3x + 16) + (2x + 8) + (4x – 18) + (2x + 25) + (3x – 7) = 720; Write the equation.
   17x + 40 = 720; Combine like terms.
   17x = 680; Subtract 40 from each side.
   x = 40; Divide each side by 17.
   136°, 136°, 88°, 142°, 105°, 113°

Measure the angles with a protractor.

Exploration 2 (page 11)

1. Sample answer:

2. Sample answer:  80°, 35°, 65°
3. Sample answer:  x = 10; 8x, 3x + 5, 6x + 5
4. Check students' work.
5. Sample answer: (16x + 4) + (6x + 4) + (23x + 2) + (13x + 2) = 360; x = 6. 100°, 40°, 140°, 80°; yes; The angles are close to those measured with a protractor.

Communicate Your Answer (page 11)

4. Connecting a vertex with each of the other vertices in a polygon creates n – 2 triangles, each of which has a total angle measure of 180°.
5. 8; solve the equation 180(n – 2) = 1080 for n.

Section 1-2 Lesson (pages 12-15)

Copy down and define all core vocabulary for this section. There is only one core concept for this section. You are learning how to solve a multi-step linear equation. It is important for you to write down all steps. Do not skip steps. Remember also, if you get stuck, you can go to Big Ideas Math (see "Textbooks and Materials" in the Course Introduction). You will have access to the odd-numbered problems and an on-line tutor.

Notice the 3 examples on pages 12-13. They are all different but they are all multi-step. Always keep in mind the end result, to isolate the variable on one side of the equation. Example 3 gives you two methods for solving. If you understand the properties and the idea of keeping the equation balanced, then you understand why both methods work. I would suggest that you follow Method 1 until you really understand symbolic manipulation.

Let’s work #9.

Now look at pages 14 and 15 for two more examples. Remember the 4-Step Problem Solving steps. These two examples model the steps. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 12-15)

1. n = –3
2. c = –20
3. x =
4. x = –6
5. d = 2.75
6. y = 5
7. x = 5
8. m = –5
9. x = 1
10. 
11. 36 ft by 12 ft