מתמטיקה תיכונית/אלגברה תיכונית/משוואות/משוואות פשוטות בנעלם אחד/תרגילים/רמה ג
מתוך ויקיספר, אוסף הספרים והמדריכים החופשי
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מתמטיקה תיכונית
|
אלגברה תיכונית
|
משוואות
|
משוואות פשוטות בנעלם אחד
|
תרגילים
קפיצה לניווט
קפיצה לחיפוש
תרגילים
[
עריכה
]
פתרו את המשוואות הבאות (ארוך)
−
11
4
x
+
3
5
+
1
5
−
1
2
x
+
1
2
+
3
4
=
−
1
2
x
+
11
4
x
+
591
20
{\displaystyle -{\frac {11}{4}}x+{\frac {3}{5}}+{\frac {1}{5}}-{\frac {1}{2}}x+{\frac {1}{2}}+{\frac {3}{4}}=-{\frac {1}{2}}x+{\frac {11}{4}}x+{\frac {591}{20}}}
4
3
−
1
3
x
+
3
7
+
12
x
=
11
9
−
x
−
4
5
+
9
2
−
57851
630
{\displaystyle {\frac {4}{3}}-{\frac {1}{3}}x+{\frac {3}{7}}+12x={\frac {11}{9}}-x-{\frac {4}{5}}+{\frac {9}{2}}-{\frac {57851}{630}}}
2
3
+
4
x
−
2
3
−
3
7
x
+
2
3
=
7
2
x
−
7
11
−
x
+
2281
231
{\displaystyle {\frac {2}{3}}+4x-{\frac {2}{3}}-{\frac {3}{7}}x+{\frac {2}{3}}={\frac {7}{2}}x-{\frac {7}{11}}-x+{\frac {2281}{231}}}
11
4
+
11
7
+
8
11
+
3
4
x
+
7
2
=
10
x
+
11
8
x
−
1
2
−
36483
308
{\displaystyle {\frac {11}{4}}+{\frac {11}{7}}+{\frac {8}{11}}+{\frac {3}{4}}x+{\frac {7}{2}}=10x+{\frac {11}{8}}x-{\frac {1}{2}}-{\frac {36483}{308}}}
−
7
+
1
2
−
3
2
=
−
5
9
−
2
+
10
7
x
−
x
+
8
7
−
442
63
{\displaystyle -7+{\frac {1}{2}}-{\frac {3}{2}}=-{\frac {5}{9}}-2+{\frac {10}{7}}x-x+{\frac {8}{7}}-{\frac {442}{63}}}
−
12
x
+
4
x
−
5
7
x
−
x
=
−
11
4
+
2
x
−
5
x
−
1
−
3279
28
{\displaystyle -12x+4x-{\frac {5}{7}}x-x=-{\frac {11}{4}}+2x-5x-1-{\frac {3279}{28}}}
−
6
11
x
−
11
3
+
x
−
7
2
x
+
1
12
x
=
−
5
7
x
−
2
3
−
9
2
x
−
691
924
{\displaystyle -{\frac {6}{11}}x-{\frac {11}{3}}+x-{\frac {7}{2}}x+{\frac {1}{12}}x=-{\frac {5}{7}}x-{\frac {2}{3}}-{\frac {9}{2}}x-{\frac {691}{924}}}
1
7
+
11
5
−
3
4
x
−
12
7
x
=
−
1
6
x
−
12
5
x
−
2
+
2
3
x
+
468
35
{\displaystyle {\frac {1}{7}}+{\frac {11}{5}}-{\frac {3}{4}}x-{\frac {12}{7}}x=-{\frac {1}{6}}x-{\frac {12}{5}}x-2+{\frac {2}{3}}x+{\frac {468}{35}}}
−
2
−
3
2
−
10
9
x
−
9
11
x
=
−
10
x
+
6
−
3
8
x
+
2
3
+
30761
264
{\displaystyle -2-{\frac {3}{2}}-{\frac {10}{9}}x-{\frac {9}{11}}x=-10x+6-{\frac {3}{8}}x+{\frac {2}{3}}+{\frac {30761}{264}}}
−
8
11
x
+
5
2
x
=
−
7
2
x
+
12
−
7
11
−
4
3
x
+
3
5
+
2
3
−
5418
55
{\displaystyle -{\frac {8}{11}}x+{\frac {5}{2}}x=-{\frac {7}{2}}x+12-{\frac {7}{11}}-{\frac {4}{3}}x+{\frac {3}{5}}+{\frac {2}{3}}-{\frac {5418}{55}}}
−
2
−
3
5
+
8
x
−
9
10
+
x
+
11
10
x
=
3
+
x
+
1391
10
{\displaystyle -2-{\frac {3}{5}}+8x-{\frac {9}{10}}+x+{\frac {11}{10}}x=3+x+{\frac {1391}{10}}}
7
9
x
+
11
8
+
3
2
x
+
5
11
−
2
5
=
−
1
3
x
−
8
9
x
+
11
10
x
−
9931
440
{\displaystyle {\frac {7}{9}}x+{\frac {11}{8}}+{\frac {3}{2}}x+{\frac {5}{11}}-{\frac {2}{5}}=-{\frac {1}{3}}x-{\frac {8}{9}}x+{\frac {11}{10}}x-{\frac {9931}{440}}}
7
12
x
−
7
3
x
−
5
11
x
=
1
3
x
+
12
5
x
−
7
12
x
−
3
4
−
3
10
−
4559
220
{\displaystyle {\frac {7}{12}}x-{\frac {7}{3}}x-{\frac {5}{11}}x={\frac {1}{3}}x+{\frac {12}{5}}x-{\frac {7}{12}}x-{\frac {3}{4}}-{\frac {3}{10}}-{\frac {4559}{220}}}
3
5
x
−
3
4
+
11
x
−
1
3
−
5
x
=
−
3
11
x
−
2
3
+
7
8
x
−
12013
330
{\displaystyle {\frac {3}{5}}x-{\frac {3}{4}}+11x-{\frac {1}{3}}-5x=-{\frac {3}{11}}x-{\frac {2}{3}}+{\frac {7}{8}}x-{\frac {12013}{330}}}
3
−
1
−
1
+
11
6
x
+
3
2
−
12
11
=
−
11
12
x
−
2
3
+
863
66
{\displaystyle 3-1-1+{\frac {11}{6}}x+{\frac {3}{2}}-{\frac {12}{11}}=-{\frac {11}{12}}x-{\frac {2}{3}}+{\frac {863}{66}}}
−
2
9
+
6
7
x
+
3
4
x
+
x
+
5
3
−
7
6
x
=
−
1
3
x
+
1
7
−
365
63
{\displaystyle -{\frac {2}{9}}+{\frac {6}{7}}x+{\frac {3}{4}}x+x+{\frac {5}{3}}-{\frac {7}{6}}x=-{\frac {1}{3}}x+{\frac {1}{7}}-{\frac {365}{63}}}
−
3
2
+
6
x
+
10
3
+
7
9
x
−
3
4
=
3
2
−
2
−
5
2
−
3025
36
{\displaystyle -{\frac {3}{2}}+6x+{\frac {10}{3}}+{\frac {7}{9}}x-{\frac {3}{4}}={\frac {3}{2}}-2-{\frac {5}{2}}-{\frac {3025}{36}}}
−
3
10
x
−
9
11
−
2
3
x
−
6
x
−
10
+
1
9
=
−
10
9
+
6
11
+
1877
495
{\displaystyle -{\frac {3}{10}}x-{\frac {9}{11}}-{\frac {2}{3}}x-6x-10+{\frac {1}{9}}=-{\frac {10}{9}}+{\frac {6}{11}}+{\frac {1877}{495}}}
12
5
x
+
1
8
x
−
11
2
+
11
3
x
=
−
1
4
x
−
5
6
x
+
8
7
−
1
3
x
+
17313
280
{\displaystyle {\frac {12}{5}}x+{\frac {1}{8}}x-{\frac {11}{2}}+{\frac {11}{3}}x=-{\frac {1}{4}}x-{\frac {5}{6}}x+{\frac {8}{7}}-{\frac {1}{3}}x+{\frac {17313}{280}}}
10
3
+
1
2
+
1
12
=
7
x
+
1
3
−
12
7
+
4
3
x
+
11
7
+
10813
84
{\displaystyle {\frac {10}{3}}+{\frac {1}{2}}+{\frac {1}{12}}=7x+{\frac {1}{3}}-{\frac {12}{7}}+{\frac {4}{3}}x+{\frac {11}{7}}+{\frac {10813}{84}}}
9
8
−
2
3
x
+
7
4
x
+
7
12
=
−
1
4
+
3
x
−
x
+
6
7
x
+
3011
168
{\displaystyle {\frac {9}{8}}-{\frac {2}{3}}x+{\frac {7}{4}}x+{\frac {7}{12}}=-{\frac {1}{4}}+3x-x+{\frac {6}{7}}x+{\frac {3011}{168}}}
−
2
5
−
4
3
−
11
2
x
−
7
6
x
−
1
3
x
−
3
11
=
10
3
x
+
6
7
+
14811
385
{\displaystyle -{\frac {2}{5}}-{\frac {4}{3}}-{\frac {11}{2}}x-{\frac {7}{6}}x-{\frac {1}{3}}x-{\frac {3}{11}}={\frac {10}{3}}x+{\frac {6}{7}}+{\frac {14811}{385}}}
11
6
x
−
3
x
+
5
−
1
6
x
−
3
8
x
=
−
6
x
+
8
5
+
11
5
+
1048
15
{\displaystyle {\frac {11}{6}}x-3x+5-{\frac {1}{6}}x-{\frac {3}{8}}x=-6x+{\frac {8}{5}}+{\frac {11}{5}}+{\frac {1048}{15}}}
9
11
+
1
4
+
2
5
−
3
4
x
+
5
4
x
−
2
+
11
3
x
=
5
2
x
−
15751
660
{\displaystyle {\frac {9}{11}}+{\frac {1}{4}}+{\frac {2}{5}}-{\frac {3}{4}}x+{\frac {5}{4}}x-2+{\frac {11}{3}}x={\frac {5}{2}}x-{\frac {15751}{660}}}
−
9
4
+
9
7
−
7
12
x
−
9
5
x
−
6
5
+
2
7
x
=
−
2
−
3
5
+
1147
105
{\displaystyle -{\frac {9}{4}}+{\frac {9}{7}}-{\frac {7}{12}}x-{\frac {9}{5}}x-{\frac {6}{5}}+{\frac {2}{7}}x=-2-{\frac {3}{5}}+{\frac {1147}{105}}}
−
9
10
+
5
11
x
−
10
−
9
7
x
−
7
+
1
=
−
4
5
+
1
5
−
9991
770
{\displaystyle -{\frac {9}{10}}+{\frac {5}{11}}x-10-{\frac {9}{7}}x-7+1=-{\frac {4}{5}}+{\frac {1}{5}}-{\frac {9991}{770}}}
−
3
8
x
+
4
3
+
3
2
+
4
11
x
=
−
2
x
+
10
7
+
2
3
x
−
5
12
−
6207
616
{\displaystyle -{\frac {3}{8}}x+{\frac {4}{3}}+{\frac {3}{2}}+{\frac {4}{11}}x=-2x+{\frac {10}{7}}+{\frac {2}{3}}x-{\frac {5}{12}}-{\frac {6207}{616}}}
−
5
11
x
−
2
x
+
8
7
−
7
10
+
7
=
8
9
x
+
11
10
+
5
4
+
54183
1540
{\displaystyle -{\frac {5}{11}}x-2x+{\frac {8}{7}}-{\frac {7}{10}}+7={\frac {8}{9}}x+{\frac {11}{10}}+{\frac {5}{4}}+{\frac {54183}{1540}}}
−
3
x
−
9
2
x
+
3
+
1
5
=
−
5
6
x
+
7
4
x
+
7
3
x
−
5
11
x
−
2089
55
{\displaystyle -3x-{\frac {9}{2}}x+3+{\frac {1}{5}}=-{\frac {5}{6}}x+{\frac {7}{4}}x+{\frac {7}{3}}x-{\frac {5}{11}}x-{\frac {2089}{55}}}
1
6
−
3
−
5
x
−
5
3
x
+
9
=
4
+
5
4
−
4
9
x
−
2207
36
{\displaystyle {\frac {1}{6}}-3-5x-{\frac {5}{3}}x+9=4+{\frac {5}{4}}-{\frac {4}{9}}x-{\frac {2207}{36}}}
11
6
x
−
1
5
x
−
1
4
−
8
5
x
+
1
2
x
+
9
5
=
−
1
5
x
+
6
5
x
+
143
20
{\displaystyle {\frac {11}{6}}x-{\frac {1}{5}}x-{\frac {1}{4}}-{\frac {8}{5}}x+{\frac {1}{2}}x+{\frac {9}{5}}=-{\frac {1}{5}}x+{\frac {6}{5}}x+{\frac {143}{20}}}
−
3
5
x
−
5
x
+
9
5
−
11
7
+
7
6
+
9
4
x
=
−
3
+
8
3
x
+
24589
420
{\displaystyle -{\frac {3}{5}}x-5x+{\frac {9}{5}}-{\frac {11}{7}}+{\frac {7}{6}}+{\frac {9}{4}}x=-3+{\frac {8}{3}}x+{\frac {24589}{420}}}
1
3
+
1
+
7
2
x
+
10
9
x
=
5
7
−
9
5
+
2
9
x
+
5
+
1753
35
{\displaystyle {\frac {1}{3}}+1+{\frac {7}{2}}x+{\frac {10}{9}}x={\frac {5}{7}}-{\frac {9}{5}}+{\frac {2}{9}}x+5+{\frac {1753}{35}}}
−
6
5
x
−
9
2
−
8
5
+
7
12
−
2
5
−
6
x
+
11
8
=
−
5
6
x
+
655
24
{\displaystyle -{\frac {6}{5}}x-{\frac {9}{2}}-{\frac {8}{5}}+{\frac {7}{12}}-{\frac {2}{5}}-6x+{\frac {11}{8}}=-{\frac {5}{6}}x+{\frac {655}{24}}}
1
+
x
−
4
11
x
+
7
2
x
−
1
6
=
−
2
3
−
2
5
x
−
3
8
x
−
1501
440
{\displaystyle 1+x-{\frac {4}{11}}x+{\frac {7}{2}}x-{\frac {1}{6}}=-{\frac {2}{3}}-{\frac {2}{5}}x-{\frac {3}{8}}x-{\frac {1501}{440}}}
−
3
2
x
−
1
7
+
x
−
1
12
x
+
x
−
3
2
−
1
8
=
1
9
x
−
2893
504
{\displaystyle -{\frac {3}{2}}x-{\frac {1}{7}}+x-{\frac {1}{12}}x+x-{\frac {3}{2}}-{\frac {1}{8}}={\frac {1}{9}}x-{\frac {2893}{504}}}
7
6
−
1
+
1
5
x
−
2
3
−
2
x
+
5
11
=
−
4
3
x
−
1
2
x
−
13
165
{\displaystyle {\frac {7}{6}}-1+{\frac {1}{5}}x-{\frac {2}{3}}-2x+{\frac {5}{11}}=-{\frac {4}{3}}x-{\frac {1}{2}}x-{\frac {13}{165}}}
x
+
1
10
+
12
+
5
8
x
=
−
7
9
+
5
12
x
−
8
9
x
+
4
11
x
+
16672
495
{\displaystyle x+{\frac {1}{10}}+12+{\frac {5}{8}}x=-{\frac {7}{9}}+{\frac {5}{12}}x-{\frac {8}{9}}x+{\frac {4}{11}}x+{\frac {16672}{495}}}
−
1
6
+
1
2
−
x
+
5
3
x
+
3
11
x
=
5
11
−
3
+
11
6
x
+
1193
66
{\displaystyle -{\frac {1}{6}}+{\frac {1}{2}}-x+{\frac {5}{3}}x+{\frac {3}{11}}x={\frac {5}{11}}-3+{\frac {11}{6}}x+{\frac {1193}{66}}}
10
7
−
4
−
9
8
x
+
4
x
−
3
8
+
9
5
x
=
x
+
5
2
x
+
596
35
{\displaystyle {\frac {10}{7}}-4-{\frac {9}{8}}x+4x-{\frac {3}{8}}+{\frac {9}{5}}x=x+{\frac {5}{2}}x+{\frac {596}{35}}}
−
3
2
x
−
8
7
+
3
8
x
−
11
7
=
11
10
x
−
10
3
−
2
−
4
3
−
4943
168
{\displaystyle -{\frac {3}{2}}x-{\frac {8}{7}}+{\frac {3}{8}}x-{\frac {11}{7}}={\frac {11}{10}}x-{\frac {10}{3}}-2-{\frac {4}{3}}-{\frac {4943}{168}}}
−
11
9
x
−
9
4
+
1
10
=
−
1
+
2
7
+
3
x
−
7
12
−
7
10
+
6634
105
{\displaystyle -{\frac {11}{9}}x-{\frac {9}{4}}+{\frac {1}{10}}=-1+{\frac {2}{7}}+3x-{\frac {7}{12}}-{\frac {7}{10}}+{\frac {6634}{105}}}
1
10
+
−
1
4
x
+
6
11
+
2
3
+
3
11
+
1
10
x
=
−
3
4
x
+
3163
330
{\displaystyle {\frac {1}{10}}+-{\frac {1}{4}}x+{\frac {6}{11}}+{\frac {2}{3}}+{\frac {3}{11}}+{\frac {1}{10}}x=-{\frac {3}{4}}x+{\frac {3163}{330}}}
−
6
7
x
−
1
10
x
+
4
+
3
2
x
−
3
11
x
=
10
+
5
2
x
+
11
9
+
212651
6930
{\displaystyle -{\frac {6}{7}}x-{\frac {1}{10}}x+4+{\frac {3}{2}}x-{\frac {3}{11}}x=10+{\frac {5}{2}}x+{\frac {11}{9}}+{\frac {212651}{6930}}}
−
7
9
x
−
1
2
x
+
5
3
x
=
4
5
+
1
−
5
7
x
+
6
5
−
1
6
−
109
63
{\displaystyle -{\frac {7}{9}}x-{\frac {1}{2}}x+{\frac {5}{3}}x={\frac {4}{5}}+1-{\frac {5}{7}}x+{\frac {6}{5}}-{\frac {1}{6}}-{\frac {109}{63}}}
5
11
+
1
+
1
5
−
x
−
11
x
+
1
+
1
12
x
=
2
5
x
+
1655
11
{\displaystyle {\frac {5}{11}}+1+{\frac {1}{5}}-x-11x+1+{\frac {1}{12}}x={\frac {2}{5}}x+{\frac {1655}{11}}}
−
11
7
−
1
4
−
3
4
−
3
4
=
8
3
−
5
7
+
13
x
−
9
8
x
−
229
14
{\displaystyle -{\frac {11}{7}}-{\frac {1}{4}}-{\frac {3}{4}}-{\frac {3}{4}}={\frac {8}{3}}-{\frac {5}{7}}+13x-{\frac {9}{8}}x-{\frac {229}{14}}}
−
1
−
5
3
−
1
2
x
−
8
11
x
=
−
1
12
+
9
5
+
1
2
+
x
+
2657
660
{\displaystyle -1-{\frac {5}{3}}-{\frac {1}{2}}x-{\frac {8}{11}}x=-{\frac {1}{12}}+{\frac {9}{5}}+{\frac {1}{2}}+x+{\frac {2657}{660}}}
−
9
4
x
−
9
5
+
11
6
x
+
8
x
−
1
5
+
2
3
+
3
7
=
9
8
x
−
3407
168
{\displaystyle -{\frac {9}{4}}x-{\frac {9}{5}}+{\frac {11}{6}}x+8x-{\frac {1}{5}}+{\frac {2}{3}}+{\frac {3}{7}}={\frac {9}{8}}x-{\frac {3407}{168}}}
5
9
−
2
x
−
2
3
x
+
3
10
x
+
9
7
=
−
4
−
3
2
−
2
3
x
+
23903
630
{\displaystyle {\frac {5}{9}}-2x-{\frac {2}{3}}x+{\frac {3}{10}}x+{\frac {9}{7}}=-4-{\frac {3}{2}}-{\frac {2}{3}}x+{\frac {23903}{630}}}
תשובות סופיות
[
עריכה
]
−
5
{\displaystyle -5}
−
7
{\displaystyle -7}
8
{\displaystyle 8}
12
{\displaystyle 12}
1
{\displaystyle 1}
18
{\displaystyle 18}
1
{\displaystyle 1}
−
16
{\displaystyle -16}
15
{\displaystyle 15}
−
13
{\displaystyle -13}
16
{\displaystyle 16}
−
10
{\displaystyle -10}
5
{\displaystyle 5}
−
6
{\displaystyle -6}
4
{\displaystyle 4}
−
4
{\displaystyle -4}
−
13
{\displaystyle -13}
−
2
{\displaystyle -2}
9
{\displaystyle 9}
−
15
{\displaystyle -15}
−
9
{\displaystyle -9}
−
4
{\displaystyle -4}
16
{\displaystyle 16}
−
14
{\displaystyle -14}
−
5
{\displaystyle -5}
−
4
{\displaystyle -4}
−
9
{\displaystyle -9}
−
9
{\displaystyle -9}
4
{\displaystyle 4}
10
{\displaystyle 10}
−
12
{\displaystyle -12}
−
9
{\displaystyle -9}
12
{\displaystyle 12}
−
5
{\displaystyle -5}
−
1
{\displaystyle -1}
−
13
{\displaystyle -13}
−
1
{\displaystyle -1}
12
{\displaystyle 12}
−
17
{\displaystyle -17}
17
{\displaystyle 17}
15
{\displaystyle 15}
−
15
{\displaystyle -15}
5
{\displaystyle 5}
−
17
{\displaystyle -17}
1
{\displaystyle 1}
−
12
{\displaystyle -12}
−
14
{\displaystyle -14}
−
4
{\displaystyle -4}
−
3
{\displaystyle -3}
−
18
{\displaystyle -18}
קטגוריה
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אלגברה תיכונית - משוואות
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