trying to solve these two problems

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

So the solution is -3 < x < 32

trying to solve these two problems

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

So the solution is -3 < x < 32

**-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.

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## Comments

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.