Chp.2－代數:解方程 Algebra-scales
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Q.1
5x －7 = 3x －21
[1]   5x －7 +7 = 3x －21 +7
[2]   5x = 3x －14
[3]   5x －3x = 3x －14 －3x
[4]   2x = －14
[5]   2x
2		 = －14
2
[6]   x = －7
 
驗證 ... LHS = 5(－7)－7 = －42
RHS = 3(－7)－21 = －42
Q.2 (通分母)
x
4		 + x
3		 = 1
[1]   (3)
(3)		 x
4		 + x
3		 (4)
(4)		 = 1
[2]   3x +4x
12		 = 1
[3]   7x = 12
[4]   x = 12
7
Q.2 (全式×12)
x
4		 + x
3		 = 1
[1]   12(  x
4		 + x
3		 ) = 1 (12)
[2]   3x +4x = 12
[3]   7x = 12
[4]   x = 12
7
驗證 ...
Q.3
2x － (x－1) = 8 + 2(x－1)
[1]   2x －x +1 = 8 +2x －2
[2]   x +1 = 6 + 2x
[3]   x +1 －x = 6 + 2x －x
[4]   1 = 6 + x
[5]   1 －6 = 6 + x －6
[6]   －5 = x
[7]   x = －5
驗證 ...
Q.4      運算次序: x－2, ×3, ÷2, +6
3
2		 (x－2) +6 = 15
[1]   3
2		 (x－2) +6 －6 = 15 －6
[2]   3
2		 (x－2) • 2
3 		= 9 ( 2
3 		)
[3]   (x－2) = 6
[4]   x－2 +2 = 6 +2
[5]   x = 8
驗證 ...
Q.5
x－1
2		 －1 = 2x－3
5		 +3
[1]   x－1
2		 －1 +1 = 2x－3
5		 +3 +1
[2]   x－1
2		 = 2x－3
5		 +4
[3]   ( x－1
2		 ) ×10 = ( 2x－3
5		 +4 ) ×10
10(x－1)
2		 = 10(2x－3)
5		 +4(10)
[4]   5 (x－1) = 2 (2x－3) +40
[5]   5x －5 = 4x －6 +40
[6]   5x －4x = －6 +40 +5
[7]   x = 39
驗證 ...