Unit 9 Review

Linear Equations

100

Is this a linear equation? 

4x - 3 = 5x²

No! The quadratic term (5x²) makes this NOT a linear equation! 

200

What could you multiply this equation by to get rid of the fractions? 

(1/2)x + (1/3)x = 10

6, 12, 18, etc. Anything that is divisible by both 2 and 3!! 6 is the LEAST COMMON MULTIPLE, so the smallest number we could use!

300

Solve the following equation: 4 + (2/3)x = 10

x = 9

400

Solve the following equation: (2/3)x - (1/4)x = 5

x = 12

500

Solve the following equation: 3( 2x + (5/3) ) = 21

x = 8/3

Absolute Value Equations

100

Is this an absolute value equation? 

|x| = 3

YES! There are absolute value lines | | around the variable. The solutions for x are: x = -3, 3

200

How many solutions does the following absolute value equation have: 

-3|2x - 4| = -12

2 solutions! If we isolate the absolute value, we get: 

|2x - 4| = 4

Since the absolute value equals a positive number, we can split it into the positive and negative case to get 2 solutions: x = 0, 4

300

How many solutions does the following absolute value equation have? 

2|x + 4| - 12 = -12

1 solution! If we isolate the absolute value, we get: 

|x + 4| = 0. 

Since the absolute value equals 0, our positive and negative cases will be the same, and therefore we will only have 1 solution: x = -4 

400

Solve the absolute value equation: 

-2 + |4 - 2x| = 6

x = -2, 6

500

Solve the absolute value equation: 

-2|5x - 7| + 6 = 18

no solution

Quadratic Equations

100

Is this a quadratic equation? 

2x² = 288

YES! There is a quadratic term (2x2) and no bigger exponents, so this is quadratic.

200

Solve the following quadratic equation: 

3x² = 75

x = -5, 5

300

Solve the quadratic equation: 

2x² + 8x = 10

x = -5, 1

400

Solve the following quadratic equation: 

13x = -2x² - 6 

x = -6, -(1/2)

500

3x² = 49

x = +/- (7 sqrt(3))/3

Free For All

100

Which equation creates a graph that looks like a V? 

(linear, quadratic, or absolute value?) 

Absolute value!

200

Do you factor to solve linear equations? 

No, we factor to solve quadratics! To solve linear equations, we use inverse operations to isolate our variable. 

300

How many solutions will the following absolute value equation have: 

|2x - 3| = -4

None! Absolute value equations can never return a negative. 

400

Is the following equation a linear equation, quadratic equation, or neither? 

y = 3^{x + 1} - 4

Neither! This is an exponential equation, like we studied in unit 8. 

Bonus (+50 pts.): Is this exponential growth or decay? 

500

Solve the following quadratic equation: 

20x² = -16x

x = -(4/5), 0