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
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
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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.
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.