SOLUTION: Solve: A. 5x-4(6+2x)<2(1-x) B. x-9<3x-4<x+8 C. 12-/7-2m/=9 (// are suppose to be absolute value sign) If all of these are solved the same way could you please just show me ho

Algebra ->  Expressions -> SOLUTION: Solve: A. 5x-4(6+2x)<2(1-x) B. x-9<3x-4<x+8 C. 12-/7-2m/=9 (// are suppose to be absolute value sign) If all of these are solved the same way could you please just show me ho      Log On


   

Question 206537: Solve:
A. 5x-4(6+2x)<2(1-x)
B. x-9<3x-4 C. 12-/7-2m/=9 (// are suppose to be absolute value sign)
If all of these are solved the same way could you please just show me how to do one. Thank you!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)


5x-4%286%2B2x%29%3C2%281-x%29 Start with the given inequality.


5x-24-8x%3C2-2x Distribute.


-3x-24%3C2-2x Combine like terms on the left side.


-3x%3C2-2x%2B24 Add 24 to both sides.


-3x%2B2x%3C2%2B24 Add 2x to both sides.


-x%3C2%2B24 Combine like terms on the left side.


-x%3C26 Combine like terms on the right side.


x%3E%2826%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E-26 Reduce.


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Answer:

So the solution is x%3E-26




B)




x-9%3C3x-4 Start with the given inequality.


x%3C3x-4%2B9 Add 9 to both sides.


x-3x%3C-4%2B9 Subtract 3x from both sides.


-2x%3C-4%2B9 Combine like terms on the left side.


-2x%3C5 Combine like terms on the right side.


x%3E%285%29%2F%28-2%29 Divide both sides by -2 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E-5%2F2 Reduce.


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Answer:

So the solution is x%3E-5%2F2


Which in decimal form is x%3E-2.5





C)

12-abs%287-2m%29=9 Start with the given equation.


-abs%287-2m%29=9-12 Subtract 12 from both sides.


-abs%287-2m%29=-3 Combine like terms.


abs%287-2m%29=3 Multiply both sides by -1.


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

7-2m=-3 or 7-2m=3 Set the expression 7-2m equal to the original value 3 and it's opposite -3


Now lets focus on the first equation 7-2m=-3


-2m=-3-7 Subtract 7 from both sides


-2m=-10 Combine like terms on the right side


m=%28-10%29%2F%28-2%29 Divide both sides by -2 to isolate m


m=5 Divide


--------------------------------


Now lets focus on the second equation 7-2m=3


-2m=3-7Subtract 7 from both sides


-2m=-4 Combine like terms on the right side


m=%28-4%29%2F%28-2%29 Divide both sides by -2 to isolate m


m=2 Divide


So the solutions are: m=5 or m=2



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
A. 5x-4(6+2x)<2(1-x)
5x-24-8x<2-2x
-3x-24 < 2-2x
Add 3x to both sides: subtract 2 from both sides
5x < -26
x < -26/5
============================
B. x-9<3x-4
Subtract x from both sides: Add 4 to both sides
2x > -5
x > -5/2
============================

C. 12-/7-2m/=9
|7-2m| = 3
7-2m = 3 or 7-2m = -3
2m = 4 or 2m = 10
m = 2 or m = 5
========================
Cheers,
stan H.