Why does decrease in fixed taxes accompanied by a decrease in Government Spending of the same amount will decrease GDP? I personally don't agree because change in GDP caused by decreased in fixed taxes should be 

$\triangle$ fixed taxes $ \times \frac{-b}{1-MPE}$(fix tax multiplier), which turns out to be a positive number while change caused by decrease of Government Spending is 

$\triangle$ Government Spending $ \times \frac{1}{1-MPE}$(autonomous multiplier) which is a negative number. Therefore I don't think we can make conclusion. Does anyone know what did I do wrong?
The question basically boils down to whether the inequality below is true or not.
$$\bigg|\Delta G\bigg(\frac{1}{1-MPC}\bigg)\bigg|&gt;\bigg|\Delta T\bigg(-\frac{MPC}{1-MPC}\bigg)\bigg|$$
If $\Delta G=\Delta T$, we can divide by either and get
$$\bigg|\bigg(\frac{1}{1-MPC}\bigg)\bigg|&gt;\bigg|\bigg(-\frac{MPC}{1-MPC}\bigg)\bigg|$$
If we multiply each side by $1-MPC$ and we evaluate the absolute value, we get
$$1&gt;MPC$$ 
This statement is true, so that implies that the first inequality is true. By this inequality, we know that $\Delta GDP_G&gt;\Delta GDP_T$. Since $\Delta GDP_G&lt;0$ and $\Delta GDP_T&gt;0\implies \Delta GDP&lt;0$