SOLUTION: Can someone please show me how to work these two examples? 0.9x + 6 ≤ 1.3x -3 The solution set should be {x|x __ __} The second is -3 ≤ 3x-2 ≤ -1, the solution

Algebra ->  Inequalities -> SOLUTION: Can someone please show me how to work these two examples? 0.9x + 6 ≤ 1.3x -3 The solution set should be {x|x __ __} The second is -3 ≤ 3x-2 ≤ -1, the solution      Log On


   

Question 221037: Can someone please show me how to work these two examples?
0.9x + 6 ≤ 1.3x -3 The solution set should be {x|x __ __}
The second is -3 ≤ 3x-2 ≤ -1, the solution set {x| __ ≤ x ≤ __}
I have been trying for hours to figure these and just can not seem to do so. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

0.9x%2B6%3C=1.3x-3 Start with the given inequality.


10%280.9x%2B6%29%3C=10%281.3x-3%29 Multiply both sides by 10 to clear out the decimals.


9x%2B60%3C=13x-30 Distribute and multiply.


9x%3C=13x-30-60 Subtract 60 from both sides.


9x-13x%3C=-30-60 Subtract 13x from both sides.


-4x%3C=-30-60 Combine like terms on the left side.


-4x%3C=-90 Combine like terms on the right side.


x%3E=%28-90%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E=45%2F2 Reduce.


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

Answer:

So the solution is x%3E=45%2F2


Which in decimal form is x%3E=22.5


So the answer in interval notation is [)


Also, the answer in set-builder notation is

================================================================
# 2

-3%3C=3x-2%3C=-1 Start with the given compound inequality.


-3%2B2%3C=3x%3C=-1%2B2 Add 2 to all sides.


-1%3C=3x%3C=-1%2B2 Combine like terms on the left side.


-1%3C=3x%3C=1 Combine like terms on the right side.


-1%2F3%3C=x%3C=1%2F3 Divide all sides by 3.


So the solution is -1%2F3%3C=x%3C=1%2F3


So the answer in interval notation is []


Also, the answer in set-builder notation is