Algebra 2 w Stats Review (2.1, 2.2, 2.3)

Properties of Equality

100

To solve equations, use the Properties of Equality to isolate the ___________ on one side.

variable

200

Which Property of Equality states, "For any real numbers a, b, and c, if a = b, then a + c = b + c"?  

Addition Property of Equality

300

Which Property of Equality states, "For any real numbers a, b, and c, if a = b, then ac = bc"?  

Multiplication Property of Equality

400

Which Property of Equality states, "For any real numbers a, b, and c, if a = b, then a - c = b - c"?

Subtraction Property of Equality

500

Which Property of Equality states, "For any real numbers a, b, and c, c ≠ 0, if a = b, then a/c = b/c"?

Division Property of Equality

Solve Each Equation

100

6x - 5 = 7 - 9x

x = 4/5

200

6y - 5 = -3(2y + 1)

y = 1/6

300

-4(10 + 3x) - (x+8) = -9

x = -3

400

The slope m between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Solve for y₂

y₂ = m(x₂ - x₁) + y₁

500

The length of a rectangle is twice the width.  Find the width if the perimeter is 60 centimeters.  Write an equation for the perimeter and solve for the width.

P = 2L + 2W = 60 cm

L = 2W

P = 2(2W) + 2W = 60

W = 10 cm

Solve Each Inequality

100

3a + 7 ≤ 16

{a | a ≤ 3}

200

20 - 3n > 7n

{n | n < 2}

300

4(5x + 7) ≤ 13

{x | x ≤ -3/4}

400

z/(-4) ≥ 2

{z | z ≤ -8}

500

7f - 9 > 3f -1

{f | f > 2}

Forms of an Equation

100

Write the equation in Standard Form.  Identify A, B, and C:

10y - 3x + 6 = 11

3x - 10y = -5

A = 3, B = -10, C = -5

200

Write the equation in Slope-Intercept Form.  Identify the slope (m) and the y-intercept (b):

14x - 7y = 21

y = 2x - 3

m = 2, b = -3

300

Write the equation in Point-Slope Form given the:

slope = -5, and the line passes through the point (-3, -8)

y + 8 = -5(x + 3)

400

Write the equation in Point-Slope Form for a line that passes through each set of points:

(2, -3) and (1, 5)

y + 3 = -8(x - 2)

or

y - 5 = -8(x - 1)

500

Write the equation in Standard Form.  Identify A, B, and C:

(2/3)y - (3/4)x + (1/6) = 0

9x - 8y = 2

A = 9, B = -8, C = 2

Solve Each Absolute Value Equation

100

Solve. Check your solutions.

|8 + p| = 2p - 3

{11}

200

Solve. Check your solutions.

5 - 3|2 + 2w| = -7

{-3, 1}

300

Solve. Check your solutions.

8x = 2|6x - 2|

{1, 1/5}

400

Solve. Check your solutions.

8z + 20 > -|2z + 4|

{z | z > -8/3}

500

Solve. Check your solutions.

-6y + 4 = |4y + 12|

{-4/5}