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1. 计算:
(1) $21+(-14)+(-17)+9$;
(2) $(-\dfrac{1}{2})×(-1\dfrac{1}{3})÷(-\dfrac{1}{12})$;
(3) $19\dfrac{15}{16}×(-16)$;
(4) $(-1)^{10}÷2+(-\dfrac{1}{2})^{3}×16$.
(1) $21+(-14)+(-17)+9$;
(2) $(-\dfrac{1}{2})×(-1\dfrac{1}{3})÷(-\dfrac{1}{12})$;
(3) $19\dfrac{15}{16}×(-16)$;
(4) $(-1)^{10}÷2+(-\dfrac{1}{2})^{3}×16$.
答案
(1)-1 (2)-8 (3)-319 (4)$-1\dfrac{1}{2}$
2. 解下列方程:
(1) $-3x + 4 = 6 - (2x - 3)$；
(2) $2 - \frac{3x + 1}{2} = \frac{2x + 3}{5}$。
(1) $-3x + 4 = 6 - (2x - 3)$；
(2) $2 - \frac{3x + 1}{2} = \frac{2x + 3}{5}$。
答案
(1)$x=-5$ (2)$x=\dfrac{9}{19}$
3. 化简:
(1) $x^2 + 3 + 5y - 4x^2 - 3y - 1$;
(2) $-2(a^2b - \dfrac{1}{4}ab^2 + \dfrac{1}{2}a^3) - (-2a^2b + 3ab^2)$.
(1) $x^2 + 3 + 5y - 4x^2 - 3y - 1$;
(2) $-2(a^2b - \dfrac{1}{4}ab^2 + \dfrac{1}{2}a^3) - (-2a^2b + 3ab^2)$.
答案
(1)$-3x^2+2y+2$ (2)$-\dfrac{5}{2}ab^2-a^3$
4. 先化简,再求值:
$-2x^2 - \frac{1}{2}[5y^2 - 2(x^2 - y^2) + 6]$,其中 $x=-3,y=-\frac{1}{2}$.
$-2x^2 - \frac{1}{2}[5y^2 - 2(x^2 - y^2) + 6]$,其中 $x=-3,y=-\frac{1}{2}$.
答案
原式$=-2x^2-\dfrac{1}{2}(5y^2-2x^2+2y^2+6) = -2x^2-\dfrac{5}{2}y^2 +x^2-y^2-3 = -x^2-\dfrac{7}{2}y^2-3$. 当 $x=-3,y=-\dfrac{1}{2}$时, 原式$=-9-\dfrac{7}{8}-3=-12\dfrac{7}{8}$.
