Deriving Equations

1. Set up the equation for solving for the intersection between the line joining (0, 0) and (1, 4) and the line x + y = 1.

2. Set up the equation for solving for the zeros of the function f(x) = 2x³ + 4x² – 17x – 3.

3. Set up the equation for solving for the time it takes to drive 432 kilometers at a speed of 65 kilometers per hour.

4. An isosceles triangle has two angles that are the same: 15 degrees. Set up the equation for solving for the other angle of the triangle.

5. Set up the equation for solving for the principal amount of a loan, if the amount of interest owed in one year is $700 and the interest rate is 5% per year.

Answers

Predicting Solutions

Without solving these equations, predict the maximum and minimum number of solutions:

1. 3x + 54 = 8x – 6

2. 4x – 7 = 4x + 20

3. 5 + 4x = 3x² + 6x

4. 10x⁵ – 47x⁴ + 3x³ – x² + 8 = 0

5. 1 = x² + 3

Answers

Review of easy equation-solving techniques.

1. How many solutions are there to:

1/_{(x² + 1)} = 0

2. What are the solutions of:

(x – 2)/_{(x² + 1)} = 0

3. What are the solutions of:

x² – 28 = 3x

4. What are the solutions of:

(x + 3)² = 25

5. Solve:

Answers

Solve for x:

1.   3x – 3 = 5 – x

2.   1/2 – 1/x = 1/x

3. x⁴ – 1 = 0

4. 5x² – 3 = 2x

5. (x² – 2x – 3)/(x + 1) = 0

Answers