SOLUTION: Solve the following a) | 2x - 9 | < 3 b) | 3x - 4 | < -13 c) | 2x - 2 | = | x + 1 |

Algebra ->  Absolute-value -> SOLUTION: Solve the following a) | 2x - 9 | < 3 b) | 3x - 4 | < -13 c) | 2x - 2 | = | x + 1 |       Log On


   

Question 59636: Solve the following

a) | 2x - 9 | < 3
b) | 3x - 4 | < -13

c) | 2x - 2 | = | x + 1 |

d) Determine which of the following points are solutions to the system

y > -2x + 1
y < 3x + 5 (-3, 2), (-1, 5), (3, 6)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following
:
a) |2x-9|<3
-3%3C2x-9%3C3
-3%2B9%3C2x-9%2B9%3C3%2B9
6%3C2x%3C12
6%2F2%3C2x%2F2%3C12%2F2
3%3Cx%3C6
b) |3x-4|<-13
No solution |x| cannot be less than 0.

c) |2x-2|=|x+1|
%282x-2%29%5E2=%28x%2B1%29%5E2 Square both sides
4x%5E2-8x%2B4=x%5E2%2B2x%2B1 Set = to 0
4x%5E2-x%5E2-8x-2x%2B4-1=x%5E2-x%5E2%2B2x-2x%2B1-1
3x%5E2-10x%2B3=0 Factor
3x%5E2-9x-x%2B3=0
3x%28x-3%29-1%28x-3%29=0
%283x-1%29%28x-3%29=0
3x-1=0 and x-3=0
3x-1+1=0+1 and x-3+3=0+3
3x=1 and x=3
3x/3=1/3 and x=3
x=1/3 and x=3
:
d) Determine which of the following points are solutions to the system

y%3E-2x%2B1
y%3C3x%2B5+ (-3, 2), (-1, 5), (3, 6)
For (-3,2)
2%3E-2%28-3%29%2B1
2%3E6%2B1
2%3E7 2 is not greater than 7 (-3,2) is not a solution.
:
For (-1,5)
5%3E-2%28-1%29%2B1
5%3E2%2B1
5%3E3 It's true for the first equation, check the second.
5%3C3%28-1%29%2B5
5%3C-3%2B5
5%3C2 5 is not less than 2 (-1,5) is not a solution of the system.
:
For (3,6)
6%3E-2%283%29%2B1
6%3E-6%2B1
6%3E-5 It's true for the first equation, check the second.
6%3C3%283%29%2B5
6%3C9%2B5
6%3C14 It's true for the second also, therefore (3,6) is a solution to the system.
Happy Calculating!!!