Algebra I Review, part 2

Homework:

Solve. This will be collected Monday (8/24).

1. 4z= 132

2. -6 = c + 4

3. x/2 = -40

4. 4.6 + z = 3.6

5. w - 5 = -13

6. -m = 5

7. c/7 + 2 = 1

8. 5(z + 3) = 12

9. 6 - 3a/2 = -6

10. 4x + 2(x - 3) = 0

11. (3 + m)/2 = 5

12. 4(t - 7) + 6 = 30

13. 12 ∙ b ∙ 13 = 338

14. 4(5n + 7) - 3n = 3(4n - 9)

15. 12 - 23c = 7(9-c)

16. 4.7(2f - 0.5) = -6(1.6f - 8.3f)

Notes:

Variable ∙ Variable = Variable2

z ∙ z = z2

Distributive Property: Multiply the number, variable or sign (+ or -) on the outside of the parenthesis to every number on the inside of the parenthesis.

Example:

z(7-2z)
7z-2z2

Classwork:

Simplify:

1. -m + 4 +7m

2. 6x - 9x +x

3. 3z + 6 - 3z - 7

4. d/5 + 2d/7

5. 3.1 + 7.5y - 8y

6. 2.5(4z - 18) + 12

7. 6h - 3h(h + 1)

8. 3 - (2x - 7)

9. 8 + 3(y - 4)

10. 9k - 2(3k - 5) - 10

11. 5(r + 1) - (r - 3)

12. x(2x - 6) + x2

13. 2(n + 8 ) + 3n(n - 5)

Algebra I Review, part 1

Homework:

Create and solve 5 single-step and 3 two-step linear equations to be turned in. Don't forget the heading!

Notes:

Basic Rules of Algebra:

Commutative: a + b = b + a; ab = ba
Associative: (a + b) + c = a + (b + c); (ab)c = a(bc)
Distributive: a(b +c) = ab + ac; a(b – c) = ab – ac
Identity: a + 0 = a; a ∙ 1 = a
Inverse: a + (-a) = 0; a ∙ 1/a = 1
Multiplication:
(-1)a = -a
(-1)(-a) = a
a ∙ 0 = 0
(-a)(b) = -ab
(-a)(-b) = ab

Equations of Lines:

Slope-intercept form: y = mx + b
General form: Ax + By + C = 0
Point-slope form: y – y1 = m(x – x1) [(x1,y1) point on line]
Horizontal line: y = b
Vertical line: x = a

Distance formula: √(x2 – x1) + (y2 – y1)
Midpoint formula: x1 + x2 , y1 + y2
2 2

Problem Solving:

1. Understand the problem. Read the problem carefully. Decide what information you are given and what information you need to find. Eliminate unnecessary information.
2. Make a plan to solve the problem. Choose a strategy. PEMA. Equation/formula. Look for a pattern. Break into simpler parts. Work backwards. Make a table.
3. Carry out the plan to solve the problem.
4. Check to see if your answer in reasonable.

Solving Linear Equations

1. Get x by itself.

x+12=25 x-6=0 -36/-9=-9x/-9

-12 -12 +6 +6 x=4

x=13 x=6

-32x/-32=4/-32 -6=x+4 3x-4=20

x=-0.125 -4 -4 +4 +4

-10=x 3x/3 24/3

x=8