怎么用分配率解方程

分配率表示的是，一个和与一个数的积，等于这个数单独乘以所有和里的数的总和。这表示a(b+c)=ab+ac。你可以用此规律来解出并简化很多方程式。想知道怎幺正确使用分配率？下面教你。

步骤

用基本分配率

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/4e\/Use-Distributive-Property-to-Solve-an-Equation-Step-1.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-1.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/4e\/Use-Distributive-Property-to-Solve-an-Equation-Step-1.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-1.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 把括号外的数乘以括号内的数字。本质上是用括号内的数字分配给括号外的数来乘。用括号外的数乘以括号内的第一个数、第二个数……如果超过两项，就一直乘下去。如下：
   • 例如： 2(x - 3) = 10
   • 2(x) - (2)(3) = 10
   • 2x - 6 = 10
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/dc\/Use-Distributive-Property-to-Solve-an-Equation-Step-2.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/dc\/Use-Distributive-Property-to-Solve-an-Equation-Step-2.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-2.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 把相似性合并。解方程前，需要把类似的项合并。把所有常数项合起来、所有含有x的项合起来。把没有变量的数字放在一边，有“x”变量的放在另一边。
   • 2x - 6(+6) = 10 (+6)
   • 2x = 16
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/25\/Use-Distributive-Property-to-Solve-an-Equation-Step-3.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/25\/Use-Distributive-Property-to-Solve-an-Equation-Step-3.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-3.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 解方程。两边同除2，得到x。
   • 2x = 16
   • 2x/2 = 16/2
   • x = 8

用更高级的分配率

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/e\/e6\/Use-Distributive-Property-to-Solve-an-Equation-Step-4.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/e\/e6\/Use-Distributive-Property-to-Solve-an-Equation-Step-4.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-4.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 把括号外的项乘以括号内的项。和基本作法一样，不过这里要多用一次分配率。
   • 例如： 4(x + 5) = 8 + 6(2x - 2)
   • 4(x) + 4(5) = 8 + 6(2x) - 6(2)
   • 4x + 20 = 8 +12x -12
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d9\/Use-Distributive-Property-to-Solve-an-Equation-Step-5.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-5.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d9\/Use-Distributive-Property-to-Solve-an-Equation-Step-5.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-5.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 合并同类项。把所有同类项合并（有x变量或无x变量的），放在等式两边。
   • 4x + 20 = 8 +12x -12
   • 4x + 20 = 12x - 4
   • 4x -12x = -4 - 20
   • -8x = -24
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/fd\/Use-Distributive-Property-to-Solve-an-Equation-Step-6.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-6.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/fd\/Use-Distributive-Property-to-Solve-an-Equation-Step-6.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-6.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 解方程。两边同除以-8，得到解。
   • -8x/-8 = -24/-8
   • x = 3

分配负系数

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/e\/e9\/Use-Distributive-Property-to-Solve-an-Equation-Step-7.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-7.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/e\/e9\/Use-Distributive-Property-to-Solve-an-Equation-Step-7.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-7.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 将括号外面的乘以括号里面的数。如果有负系数，就分配到每个积上。如果负数乘以正数，就会得到负数，如果负乘负，就会得到正数。^[1]
   • 例如： -4(9 - 3x) = 48
   • -4(9) - -4(3x) = 48
   • -36 -(-12x) = 48
   • -36 + 12x = 48
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/ff\/Use-Distributive-Property-to-Solve-an-Equation-Step-8.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-8.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/ff\/Use-Distributive-Property-to-Solve-an-Equation-Step-8.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-8.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 合并同类项。把所有同类项合并（有x变量或无x变量的），放在等式两边。
   • -36 + 12x = 48
   • 12x = 48 - -(36)
   • 12x = 84
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/25\/Use-Distributive-Property-to-Solve-an-Equation-Step-9.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-9.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/25\/Use-Distributive-Property-to-Solve-an-Equation-Step-9.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-9.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 解方程。两边同除以12，得到x。
   • 12x/12 = 84/12
   • x = 7

简化方程式

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/14\/Use-Distributive-Property-to-Solve-an-Equation-Step-10.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-10.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/14\/Use-Distributive-Property-to-Solve-an-Equation-Step-10.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-10.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 找出分母最小公倍数（LCM）。要找最小公倍数，就是找两个数倍数中相同且最小的一个。这里有3和6，6是最小公倍数，可以整除3，也可以整除6。^[2]
   • x - 3 = x/3 + 1/6
   • LCM = 6
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d1\/Use-Distributive-Property-to-Solve-an-Equation-Step-11.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-11.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d1\/Use-Distributive-Property-to-Solve-an-Equation-Step-11.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-11.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 把所有项乘以最小公倍数。现在等式两边所有的项都放进括号，旁边乘一个最小公倍数。然后乘以（或分配到）所有的括号内的数。两边同时乘以一个数，得到的答案是一样的。但是这样会更好解一点。
   • 6(x - 3) = 6(x/3 + 1/6)
   • 6(x) - 6(3) = 6(x/3) + 6(1/6)
   • 6x - 18 = 2x + 1
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/49\/Use-Distributive-Property-to-Solve-an-Equation-Step-12.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-12.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/49\/Use-Distributive-Property-to-Solve-an-Equation-Step-12.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-12.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 合并同类项。把所有同类项合并（有x变量或无x变量的），放在等式两边。
   • 6x - 2x = 1 - (-18)
   • 4x = 19
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a5\/Use-Distributive-Property-to-Solve-an-Equation-Step-13.jpg\/v4-460px-Use-Distributive-Property-to-Solve-an-Equation-Step-13.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a5\/Use-Distributive-Property-to-Solve-an-Equation-Step-13.jpg\/v4-728px-Use-Distributive-Property-to-Solve-an-Equation-Step-13.jpg","smallWidth":460,"smallHeight":306,"bigWidth":728,"bigHeight":485,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 解答案。两边同时除以4，得到x。
   • 4x/4 = 19/4
   • x = 19/4 或 16 3/4