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

Question

trying to solve these two problems

Answer 1

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

 

 So the solution is   -3 < x < 32

Answer 2

-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

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-(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.