Đáp án:
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Bài `1.`
`a,`
`1/7 + 2/5`
`= 19/35`
`b,`
`2/3 + (1/7 -2/3)`
`= 2/3 + 1/7 - 2/3`
`= (2/3-2/3) + 1/7`
`= 0 + 1/7`
`= 1/7`
`c,`
`2/5 - (2/5 + 1/3)`
`= 2/5 - 2/5 - 1/3`
`= (2/5-2/5) - 1/3`
`= 0-1/3`
`= (-1)/3`
`d,`
`3/5 × 11/9 + 3/5 × (-2)/9`
`= 3/5 × (11/9 + (-2)/9)`
`= 3/5 × 1`
`= 3/5`
`e,`
`4/7 × (-11)/21 - 4/7 × 6/21 - 4/7 × 6/21`
`= 4/7 × ( (-11)/21 - 6/21 - 6/21)`
`= 4/7 × (-23)/21`
`= (-92)/147`
`f,`
`3/17 × 22/19 - 3/17 × 10/19 - 3/17 × 12/19`
`= 3/17 × (22/19 - 10/19 - 12/19)`
`= 3/17 × 0`
`= 0`
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Bài `2.`
`a,`
`3/7x - 1/5=1/6`
`↔ 3/7x = 1/6 +1/5`
`↔ 3/7x = 11/30`
`↔x=11/30÷3/7`
`↔x=11/30×7/3`
`↔x=77/90`
Vậy `x=77/90`
`b,`
`1/8 -2/9x =3/7`
`↔ 2/9x = 1/8 - 3/7`
`↔ 2/9x = (-17)/56`
`↔x=(-17)/56 ÷ 2/9`
`↔x=(-17)/56 × 9/2`
`↔x=(-153)/112`
Vậy `x=(-153)/112`
`c,`
`1/3 - 1/2 (x + 1/13) = 2/3`
`↔ 1/2 (x+1/13)=1/3-2/3`
`↔1/2 (x+1/13) = (-1)/3`
`↔x+1/13=(-1)/3÷1/2`
`↔x+1/13 = (-2)/3`
`↔x=(-2)/3-1/13`
`↔x=(-29)/39`
Vậy `x=(-29)/39`
`d,`
`3/7 - 1/3 (x+1/2)=13/7`
`↔ 1/3 (x+1/2) = 3/7 - 13/7`
`↔ 1/3 (x+1/2) = (-10)/7`
`↔ x + 1/2 = (-10)/7 ÷ 1/3`
`↔ x + 1/2 = (-30)/7`
`↔x=(-30)/7 - 1/2`
`↔x=(-67)/14`
Vậy `x=(-67)/14`
`e,`
`2/9 - 1/2 (x-1/7) = (-7)/9`
`↔ 1/2 (x-1/7) = 2/9 - (-7)/9`
`↔ 1/2 (x-1/7) = 1`
`↔x-1/7=1÷1/2`
`↔x-1/7=2`
`↔x=2+1/7`
`↔x=15/7`
Vậy `x=15/7`
`f,`
`2/7 |x-1/3| - 1/7 = 6/7`
`↔ 2/7 |x-1/3| = 6/7 + 1/7`
`↔ 2/7 |x-1/3| = 1`
`↔|x-1/3| =1÷2/7`
`↔|x-1/3|=7/2`
Trường hợp 1 :
`↔x-1/3=7/2`
`↔x=7/2 + 1/3`
`↔x=23/6`
Trường hợp 2 :
`↔x-1/3=(-7)/2`
`↔x=(-7)/2 + 1/3`
`↔x=(-19)/6`
Vậy `x=23/6` hoặc `x=(-19)/6`
`g,`
`1/2 - 1/3 |x+1/2| = 1/3`
`↔ 1/3 |x+1/2| = 1/2 - 1/3`
`↔ 1/3 |x+1/2| = 1/6`
`↔|x+1/2|=1/6÷1/3`
`↔|x+1/2| = 1/2`
Trường hợp 1 :
`↔x+1/2=1/2`
`↔x=1/2-1/2`
`↔x=0`
Trường hợp 2 :
`↔x+1/2=(-1)/2`
`↔x=(-1)/2-1/2`
`↔x=-1`
Vậy `x=0` hoặc `x=-1`
