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 the Explorations 1 and 2 and Communicate Your Answer on page 245. Here are other ways to solve equations with variables on both sides. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 245)

1. y = 2x – 1; y = + 4

2. 
   x = 2

3. The two sides of the equation are equal to each other. If you set one side of the equation equal to y, the transitive property allows you to set the other side of the equation equal to y.

Exploration 2 (page 245)

1. x = –4; yes
2. x = –3; yes
3. x = 3; yes
4. x = 2; yes
5. x = 1; yes
6. x = 0; yes

Communicate Your Answer (page 245)

3. Write two linear equations setting y equal to each side. Solve the system of linear equations. The x-value of the solution of the system of linear equations is the solution of the equation.
4. The algebraic method will always give the exact solution, but it is difficult to work with fractions as coefficients. The graphical method is easier with fractional coefficients of x because these are the slopes of the lines, but solutions may sometimes be estimates, especially when the solution does not fall on a grid line.

Section 5-5 Lesson (pages 246-248)

Solving a system by graphing can now be used to solve a problem from an earlier lesson. Specifically, solving an equation with variables on both sides. The approach in this lesson is to treat each side of the equation as a function, thus creating a system of two equations in two variables.

Study and read through Examples 1 through 3. You will use your graphing calculator. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 246-248)

1. x = –2
2. x =  
3. 3 years
4. 200 miles