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solve -9 x+8<35 and -(1/4)x+2>=10

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2 Answers

I submit that these are NOT two problems, but one system of inequalities.


 So the solution is   -3 < x < 32


You may be right, and I would agree if the OP would shed some light on this. One correction to make though is that you misread the second inequality. The answers should come out as:

x > -3 and x =< -32

Thus, x cannot be in the middle of the two numbers, there is no convergence.

-9x + 8 < 35

1. Subtracting or adding negative numbers does not have any effect on direction of sign. 

     -9x < 27

2. Remember that division or multiplication by negative number makes sign flip the opposite way

     x > -3


-(1/4)x +2 >= 10


1. adding or subtracting a negative number to the other side does not change direction of sign.

         -(1/4)x >= 10-2

2.      -(1/4)x >= 8

3. Multiplying or dividing a negative number does change direction of sign and this applies to less than or equal to sign and the more than or equal to sign as well

         x =< -32


Both problems are similar to each other. The only thing you have to keep in mind is when the direction of the sign changes.