最新解一元一次不等式教案名师优秀教案.doc
解一元一次不等式教案解一元一次不等式教案 一、教学目标 1.掌握会用不等式基本性质解不等式 2.会用数轴表示出不等式的解集. 二. 重点:掌握不等式解法 三(难点:熟练应用不等式基本性质解不等式 四(关键: 1.不等式的性质二:不等式两边都乘以(或除以)同一个正数，不等号的方向不变. 2.不等式的性质三:不等式的两边都乘以(或除以)同一个负数，不等号方向改变. 五.教学过程: y,12y,21.引入:解方程,1(学生演示) 64解: 去分母(同乘最简公分母12),得:2(y-1)-3(2y-2)=-12 去括号得: 2y-2-6y+6=-12 移项得: 2y-6y=-12+2-6 合并同类项得: -4y=-16 化系数为1 (同除以-4)得:y=4 小结:解一元一次方程的基本步骤:(,)(去分母(,).去括号(,).移项(,).合并同类项(,).系数化, 2. 用不等式基本性质解不等式、 y,12y,2,1例1解不等式:并把它的解集在数轴上表示出来(学生演示) 64解: 去分母(同乘最简公分母12，方向不变),得:2(y-1)-3(2y-2)-12 ,去括号得: 2y-2-6y+6-12 ,移项得:2y-6y-12+2-6 ,合并同类项得: -4y-16 ,化系数为1(同除以-4方向改变)得:y4 ,?原不等式的解集为y4 ,这个不等式的解集在数轴上的表示如图 3 4 5 6 7 8 -1 0 1 2 小结:解一元一次不等式和解一元一次方程类似, ,(去分母(同乘负数时，方向改变) ,(去括号 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG . Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 12 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury ,. 移项 ,. 合并同类项 ,. 系数化为 系数化为1(同除以负数.方向改变)等步骤. 区别在哪里: 在去分母和系数化为1的两步中,要特别注意不等式的两边都乘以(或除以)一个负数时,不等号的方向必须改变. 3.当堂训练:解下列不等式并把它的解集在数轴上表示出来(学生演示) xx,1x,1x，2(1),1(x,-3) (2)x-?2-(x?1) ,2233x,12x，3x，52x，11(3)(x?7) (4)1-(x?-) ,1,x322324. (1)学生错题辨析: 【例1】 解不等式3x+2(2-4x)<19.【例2】 解不等式5x-3(2x-1)>-6. 错解: 去括号，得3x+4-4x<19， 错解: 去括号，得5x-6x-3>-6， 解得x>-15. 解得x<3. 【例3】 解不等式 4x-5<2x-9. 【例4】 解不等式 错解: 移项，得 4x+2x<-9-5， 错解: 去分母，得6x-2x-5>14， 即6x<-14， 解得 所以 【例5】解不等式3x,6,1+7x. 【例6】 解不等式3-5(x-2)-4(-1+5x)<0.错解:移项，得 3x,7x,1+6， 错解: 去括号，得3-x-2-4+5x<0， 即 ,4x,7 即4x<3， 所以 所以 【例7】 解不等式 错解:去分母，得3+2(2-3x)?5(1+x). 即11x?2， 所以 (2)教师错题剖析: (1)、去括号时，错用乘法分配律 【例1】 解不等式 3x+2(2-4x)<19. 错解: 去括号，得3x+4-4x<19， 解得x>-15. 诊断: 错解在去括号时，括号前面的数2没有乘以括号内的每一项. 1997 steel welded atmospheric pressure vessel 4 GB50231-T47352005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ -98 2 GB50128-quipment installation engineering 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical e-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-lding procedure qualification for steel pressure vessels 7 JB/47092000 of we-2004 petrochemical JB/ T4708-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-HGJ222ning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injuryconcerunished 12 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly pn the Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 fine oing gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a struction standard 7, HG . Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, us2000 construction installation engineering con-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-l equipment installation engineering construction and acceptance specification for 5 GB502752009 mechanica-2 正解: 去括号，得3x+4-8x<19， -5x<15， 所以x>-3. ?原不等式的解集为x>-3. (2)去括号时，忽视括号前的负号 【例2】 解不等式 5x-3(2x-1)>-6. 错解: 去括号，得5x-6x-3>-6， 解得x<3. 诊断: 去括号时，当括号前面是“-”时，去掉括号和前面的“-”，括号内的各项都要改变符号.错解在去括号时，没有将括号内的项全改变符号. 正解: 去括号，得5x-6x+3>-6， 所以-x>-9， 所以x<9. (3)、移项时，不改变符号 【例3】 解不等式 4x-5<2x-9. 错解: 移项，得 4x+2x<-9-5， 即6x<-14， 所以 诊断: 一元一次不等式中的移项和一元一次方程中的移项一样，移项就要改变符号，错解忽略了这一点. 正解: 移项，得4x-2x<-9+5， 解得2x<-4， 所以x<-2. (4)、去分母时，忽视分数线的括号作用 【例4】 解不等式 错解: 去分母，得6x-2x-5>14， 解得 诊断: 去分母时，如果分子是一个整式，去掉分母后要用括号将分子括起来.错解在去掉分母时，忽视了分数线的括号作用. 正解: 去分母，得6x-(2x-5)>14， 去括号，得6x-2x+5>14， 解得 (5)、不等式两边同除以负数，不改变方向 【例5】 解不等式3x,6,1+7x. -98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-vessel 4 GB502311997 steel welded atmospheric pressure -T47352005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ -98 2 GB50128-f welded plate II, mechanical equipment installation engineering 1 GB1502000 steel pressure vessel products mechanical properties test o-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-rochemical JB/ T47082004 pet-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-HGJ222) personal injuryy of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2bilitinjuries fatalities directly punished 12 million. Direct responsibility for the accident and have the corresponding responsi ce with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1)cordanthe responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in acsponsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, es, recylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measuron installation engineering construction standard 7, HG . Pressure gauges, using an installed spark arrestor for acetylene 2000 constructi3 错解: 移项，得 3x,7x,1+6， 即 ,4x,7， 所以 诊断:将不等式,4x,7的系数化为1时，不等式两边同除以,4后，根据不等式的基本性质:不等式两边同乘以或同除以同一个负数，不等号要改变方向，因此造成了错解. 正解: 移项，得3x,7x<1+6， 即,4x,7， 所以x, 【例6】 解不等式3-5(x-2)-4(-1+5x)<0. 错解: 去括号，得3-x-2-4+5x<0， 即4x<3， 所以 诊断: 本题一是去括号后各项没有改变符号;二是一个数乘以一个多项式时应该把这个数和多项式的每一项相乘. 正解:去括号得3-x+10+4-20x<0， 即-21x<-17，所以 【例7】 解不等式 错解:去分母，得3+2(2-3x)?5(1+x). 即11x?2， (一)情感与态度：所以 最值：若a>0，则当x=时，；若a<0，则当x=时，错误的原因是在去分母时漏乘了不含分母的一项“3”. 一年级下册数学教学工作计划正解:去分母，得30+2(2-3x)?5(1+x). 即11x?29， 4、初步学会应用加减法解决生活中简单问题，感受数学在日常生活中的作用,感受加减法与日常生活的密切联系,同时获得一些初步的数学活动经验，发展解决问题和运用数学进行思考的能力。所以 5.当堂测试:解下列不等式并把它的解集在数轴上表示出来(学生演示) xa，32,a1,(1).2-,(a,-1) (2).1-x?(x+1)(x?1) 23632x，53x，12，213,x3x，8,x,1(3).(x?-1) (4).x-,(x,6) 276438、加强作业指导、抓质量。5x，12x，12,xx,19x,5,2(5).-,-1(x,-) (6).,(x,1) 362246顶点坐标：（，）1,2x4,3xx，1x，2x，3,，(7).+-3?0(x?1) (8).(x?-2) 23436(9).2(2x-3),5(x-1)(x,-1) (10). 2-5x?8-2x(x?-2) 定义：在RtABC中，锐角A的对边与邻边的比叫做A的正切，记作tanA，l equipment installation engineering construction and acceptance specification for 5 GB502752009 mechanica-1997 steel welded atmospheric pressure vessel 4 GB50231-T47352005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ -98 2 GB50128-quipment installation engineering 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical e-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-lding procedure qualification for steel pressure vessels 7 JB/47092000 of we-2004 petrochemical JB/ T4708-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-HGJ222ning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injuryconcerunished 12 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly pn the Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 fine oing gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a struction standard 7, HG . Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, us2000 construction installation engineering con-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-4 (11).3,6+2x(x,1)(12).3(x+2)-1?8-2(x-1)(x?1) ,，x,2x,23.确定二次函数的表达式：（待定系数法）(13).3(1-x),2(x+9)(x,-3) (14).5x-12?2(4x-3)(x?-2) 6.小结:解一元一次不等式注意:(1)不等式的两边都乘以(或除以)一个负数时,不等号的方向必须改变. (2)在数轴上表示不等式的解集时注意界点表示。 （1) 与圆相关的概念：7.课后巩固:书 6、因材施教，重视基础知识的掌握。98 2 GB50128-f welded plate II, mechanical equipment installation engineering 1 GB1502000 steel pressure vessel products mechanical properties test o-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-rochemical JB/ T47082004 pet-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-HGJ222) personal injuryy of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2bilitinjuries fatalities directly punished 12 million. Direct responsibility for the accident and have the corresponding responsi ce with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1)cordanthe responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in acsponsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, es, recylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measuron installation engineering construction standard 7, HG . Pressure gauges, using an installed spark arrestor for acetylene 2000 constructi-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-vessel 4 GB502311997 steel welded atmospheric pressure -T47352005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ -5
