1. 方程中的某些项改变符号后,可以从方程的一边移到
另一边
,这样的变形叫作移项.答案：另一边
2. 移项的依据是
随堂小练
等式的基本性质
;移项时一般将含未知数的项向等号左边
移,将常数项向等号右边
移.随堂小练
答案：等式的基本性质 左边 右边
1. (2024·广水期末)解方程$3x + 4 = 4x - 5$时,移项正确的是 (
A.$3x - 4x = -5 - 4$
B.$3x + 4x = 4 - 5$
C.$3x + 4x = 4 + 5$
D.$3x - 4x = -5 + 4$
A
)A.$3x - 4x = -5 - 4$
B.$3x + 4x = 4 - 5$
C.$3x + 4x = 4 + 5$
D.$3x - 4x = -5 + 4$
答案：A
解析：
解：解方程$3x + 4 = 4x - 5$，移项得$3x - 4x = -5 - 4$。
答案：A
答案：A
2. 解方程:
(1)$x - 9 = 8$;
(2)$5 - x = -16$;
(3)$3x + 4 = -13$;
(4)$\frac{2}{3}x - 1 = 5$.
(1)$x - 9 = 8$;
(2)$5 - x = -16$;
(3)$3x + 4 = -13$;
(4)$\frac{2}{3}x - 1 = 5$.
答案：(1)$x=17$ (2)$x=21$ (3)$x=-\frac{17}{3}$ (4)$x=9$
解析：
(1)解：$x=8+9$
$x=17$
(2)解：$-x=-16-5$
$-x=-21$
$x=21$
(3)解：$3x=-13-4$
$3x=-17$
$x=-\frac{17}{3}$
(4)解：$\frac{2}{3}x=5+1$
$\frac{2}{3}x=6$
$x=6×\frac{3}{2}$
$x=9$
$x=17$
(2)解：$-x=-16-5$
$-x=-21$
$x=21$
(3)解：$3x=-13-4$
$3x=-17$
$x=-\frac{17}{3}$
(4)解：$\frac{2}{3}x=5+1$
$\frac{2}{3}x=6$
$x=6×\frac{3}{2}$
$x=9$
3. 解方程:
(1)$3 - 2x = 9 + x$;
(2)$5x - 1 = 2x + 3$;
(3)$6x - 7 = 4x - 5$;
(4)$\frac{1}{2}x - 6 = \frac{3}{4}x$;
(5)$3x + 5 = 4x + 1$;
(6)$9 - 3y = 5y + 5$.
(1)$3 - 2x = 9 + x$;
(2)$5x - 1 = 2x + 3$;
(3)$6x - 7 = 4x - 5$;
(4)$\frac{1}{2}x - 6 = \frac{3}{4}x$;
(5)$3x + 5 = 4x + 1$;
(6)$9 - 3y = 5y + 5$.
答案：(1)$x=-2$ (2)$x=\frac{4}{3}$ (3)$x=1$ (4)$x=-24$ (5)$x=4$ (6)$y=\frac{1}{2}$
解析：
(1)解：$3 - 2x = 9 + x$
$-2x - x = 9 - 3$
$-3x = 6$
$x = -2$
(2)解：$5x - 1 = 2x + 3$
$5x - 2x = 3 + 1$
$3x = 4$
$x = \frac{4}{3}$
(3)解：$6x - 7 = 4x - 5$
$6x - 4x = -5 + 7$
$2x = 2$
$x = 1$
(4)解：$\frac{1}{2}x - 6 = \frac{3}{4}x$
$\frac{1}{2}x - \frac{3}{4}x = 6$
$\frac{2}{4}x - \frac{3}{4}x = 6$
$-\frac{1}{4}x = 6$
$x = -24$
(5)解：$3x + 5 = 4x + 1$
$3x - 4x = 1 - 5$
$-x = -4$
$x = 4$
(6)解：$9 - 3y = 5y + 5$
$-3y - 5y = 5 - 9$
$-8y = -4$
$y = \frac{1}{2}$
$-2x - x = 9 - 3$
$-3x = 6$
$x = -2$
(2)解：$5x - 1 = 2x + 3$
$5x - 2x = 3 + 1$
$3x = 4$
$x = \frac{4}{3}$
(3)解：$6x - 7 = 4x - 5$
$6x - 4x = -5 + 7$
$2x = 2$
$x = 1$
(4)解：$\frac{1}{2}x - 6 = \frac{3}{4}x$
$\frac{1}{2}x - \frac{3}{4}x = 6$
$\frac{2}{4}x - \frac{3}{4}x = 6$
$-\frac{1}{4}x = 6$
$x = -24$
(5)解：$3x + 5 = 4x + 1$
$3x - 4x = 1 - 5$
$-x = -4$
$x = 4$
(6)解：$9 - 3y = 5y + 5$
$-3y - 5y = 5 - 9$
$-8y = -4$
$y = \frac{1}{2}$