Without actually performing the operations, determine mentally the coefficient of the \( x^{2} \)-term in the simplified form of the following expression. \( \left(-5 x^{2}+2 x-4\right)-\left(-2 x^{2}+x-3\right)+\left(-7 x^{2}+2 x-4\right) \) The coefficient of the \( x^{2} \)-term is \( \square \). (Type an integer or a decimal.)

To find the coefficient of the \( x^{2} \)-term, we need to focus on the \( x^{2} \) components of each polynomial in the expression. Starting with the first polynomial, \( -5x^{2} \), the coefficient is \( -5 \). For the second polynomial, \( -2x^{2} \), the coefficient is \( -2 \), but since it is subtracted, we consider it as \( +2 \). Finally, from the third polynomial, \( -7x^{2} \), the coefficient is \( -7 \). Now, we sum these coefficients: \[ -5 + 2 - 7 = -10. \] Thus, the coefficient of the \( x^{2} \)-term is \( \boxed{-10} \).