# Week 2: Equations – Day 5

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.

# Week 2: Equations – Day 4

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

# Week 2: Equations – Day 3

Equations Involving Exponential Expressions

Exponential expressions have two basic parts: exponent and base. The simplest equations involve one or the other.

1. If 2300 x 2n = 2501 what is n?

2. If 2100 x 3100 = a100 what is a?

3. If 100n x 53 = 20n x 563 what is n?

4. If 249 x 2n = 1/4, what is n?

5. If (2n)10 = 326 what is n?

# Week 2: Equations – Day 2

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: # Week 2: Equations – Day 1

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