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Algebra algebra algebra?

Published by: wktd 2009-01-08

slove (1). -9n=450 (2). -2z+5=7 (3)1/5y-2/3=6 (4) 8y-(5y-9)+-160
(5) -8y≤-40 (6) 2x-9≤9x+4
(7) a 14m picece of cable is cut into 2 pices. one pices is 4m longer than the other. how long are the pices?
(8) find the distance between points with coordinates 33 and -12.

FYI: I always rewrite equations so that subtraction is adding the opposite - that way I don't lose track of the negative signs.

(1) -9n = 450
-->divide both sides by -9 to find n
-9n/-9 = 450/-9
n = -50

(2) -2z + 5 = 7
-->add -5 to both sides to get z term alone
-2x + 5 + -5 = 7 + -5
-2z = 2
-->divide both sides by -2 to get z alone
-2z/-2 = 2/-2
z = -1

(3) 1/5y + -2/3 = 6
-->add 2/3 to both sides:
1/5y + -2/3 + 2/3 = 6 + 2/3
1/5 y = 6 2/3 -->change 6 /2/3 to improper fraction = 20/3
1/5y = 20/3
-->multiply both sides by 5 to get y alone (reciprocal of 1/5 i= 5/1 = 5)
1/5y*5 = 20/3 * 5
y = (20*5)/3
y = 100/3 = 33 1/3

(4) 8y-(5y-9)+-160
8y + -1(5y + -9) + -160
-->multiply through ()
8y + -1*-5y + -1*-9 + -160
8y + -5y + 10 + -160
-->combine like terms
3y + -150

(5) -8y ≤ -40
-->divide both sides by -8: because you are DIVIDING by a negative, flip the ≤ around to be >=

Algebra Montpellier Announcements::
AMA Algebra Montpellier Announcements. Annonces de Montpellier en Algèbre. 02- 2005 · AUTHOR · Bitjong Ndombol. Choose your nearest mirror site
http://www.emis.de/journals/AMA/HOME

Math Study Guides - SparkNotes::
Algebra I. Expressions and Equations · Applications of Solving Equations · Inequalities · Compound Inequalities · Absolute Value · Probability
http://www.sparknotes.com/math/HOME

-8y/-8 >= -40/-8
y >= 5

(6) 2x + -9 ≤ 9x+4
->move 2x by adding -2x to both sides
2x + -9 + -2x ≤ 9x + 4 + -2x
-9 ≤ 7x + 4
-->add -4 to both sides: do NOT flip the symbol because you are not multiply/divide by a neg
-9 + -4 ≤ 7x + 4 + -4
-13 ≤ 7x
-->divide both sides by 7 - do NOT flip the symbol
-13/7 ≤ 7x/7
-13/7 ≤ x

(7) x is first piece; x+4 is second piece
x + x + 4 = 14
2x + 4 = 14
2x + 4 + -4 = 14 + -4
2x = 10
2x/2 = 10/2
x = 5 first piece; second piece is x + 4 = 5 + 4 = 9
CHECK: does 5 + 9 = 14? yes

(8) 33 and -12....subtract 33 - -12 = 33 + 12 = 45
why? because there are 12 points from -12 to 0, and then 33 more points from 0 to 33....33 +12 = 45

2) -1
7)One piece is nine and the other is five.

1. -9n = 450
Divide both sides by -9
n = -50

2. -2z + 5 = 7
Subtract 5 from both sides
-2z = 2
Divide both sides by -2
z = -1

3. 1/5y - 2/3 = 6
Add 2/3 on both sides
1/5y = 6 2/3
Divide 1/5 from both sides
y = 33.3

4. 8y - (5y - 9) + -160
Distribute the negative sign
8y - 5y + 9 + -160
Combine like terms
3y - 151

5. -8y ≤ -40
Divide both sides by -8 (Remember to flip the sign)
y > or equal to 5

6. 2x - 9 ≤ 9x + 4
Add 9 to both sides
2x ≤ 9x + 13
Subtract 9x from both sides
-7x ≤ 13
Divide both sides by 13 (flip sign)
x > or equal to 1.86

7. x + 4x = 14
5x = 14
x = 2.8
Piece one = 2.8
Piece two = 11.2

8. 45