Tìm x, biết
1. $\frac{3}{x-1}$ = $\frac{21}{16}$
2. $\frac{1,2}{30}$ = $\frac{3x+4}{50}$
3. $\frac{x-1}{x-5}$ = $\frac{6}{7}$
4. $\frac{x-1}{3}$ = $\frac{x+3}{5}$
5. $\frac{3}{7}$ = $\frac{2x+1}{3x+5}$
6. $\frac{2x+3}{6}$ = $\frac{7x-3}{15}$
7. $\frac{6x-5}{-7}$ = $\frac{5x-3}{-5}$
Giúp mình với mai đi học rồi
Giải thích các bước giải:
1. `3/(x-1) = 21/16`
`⇔ 16 . 3 = 21(x-1)`
`⇔ 48 = 21x – 21`
`⇔ 21x = 69 ⇔ x = 23/7`
Vậy `x=23/7`
__________
2. `(1,2)/30 = (3x+4)/50`
`⇔ 3x + 4 = (1,2)/30 . 50`
`⇔ 3x + 4 = 2`
`⇔ 3x = -2`
`⇔ x = -2/3`
Vậy `x=(-2)/3`
_________
3. `(x-1)/(x-5) = 6/7`
`⇔ 7(x-1) = 6(x-5)`
`⇔ 7x – 7 = 6x – 30`
`⇔ x = -23`
Vậy `x=-23`
__________
4. `(x-1)/3 = (x+3)/5`
`⇔ 5(x-1) = 3(x+3)`
`⇔ 5x – 5 = 3x + 9`
`⇔ 2x = 14`
`⇔ x=7`
Vậy `x=7`
__________
5. `3/7 =(2x+1)/(3x + 5)`
`⇔ 3(3x + 5) = 7(2x + 1)`
`⇔ 9x + 15 = 14x + 7`
`⇔ -5x = -8`
`⇔ x = 8/5`
Vậy `x=8/5`
__________
6. `(2x + 3)/6 = (7x – 3)/15`
`⇔ 15(2x + 3) = 6(7x-3)`
`⇔ 30x + 45 = 42x – 18`
`⇔ -12x = -63`
`⇔ x=21/4`
Vậy `x=21/4`
__________
7. `(6x – 5)/-7 = (5x – 3)/-5`
`⇔ -7(5x – 3) = -5(6x – 5)`
`⇔ -35x + 21 = -30x + 25`
`⇔ -5x = 4`
`⇔ x = -4/5`
Vậy `x=-4/5`
__________
Đáp án:
\(1)\ x=\dfrac{23}7\\ 2)\ x=\dfrac{-2}3\\ 3)\ x=-23\\ 4)\ x=7\\ 5)\ x=\dfrac85\\ 6)\ x=\dfrac{21}4\\ 7)\ x=\dfrac{-4}5\)
Giải thích các bước giải:
\(1)\ \dfrac3{x-1}=\dfrac{21}{16}\\ ⇔21(x-1)=3.16\\ ⇔x-1=\dfrac{3.16}{21}\\ ⇔x-1=\dfrac{16}{7}\\ ⇔x=\dfrac{23}{7}\\ \text{Vậy x = $\dfrac{23}{7}$}\\ 2)\ \dfrac{1,2}{30}=\dfrac{3x+4}{50}\\ ⇔30(3x+4)=1,2.50\\ ⇔30(3x+4)=60\\ ⇔3x+4=2\\ ⇔3x=-2\\ ⇔x=\dfrac{-2}3\\ \text{Vậy x = $\dfrac{-2}3$}\\ 3)\ \dfrac{x-1}{x-5}=\dfrac67\\ ⇔7(x-1)=6(x-5)\\ ⇔7x-7=6x-30\\ ⇔7x-6x=-30+7\\ ⇔x=-23\\ \text{Vậy x = (- 23)}\\ 4)\ \dfrac{x-1}3=\dfrac{x+3}5\\ ⇔5(x-1)=3(x+3)\\ ⇔5x-5=3x+9\\ ⇔5x-3x=9+5\\ ⇔2x=14\\ ⇔x=7\\ \text{Vậy x = 7}\\ 5)\ \dfrac{3}7=\dfrac{2x+1}{3x+5}\\ ⇔3(3x+5)=7(2x+1)\\ ⇔9x+15=14x+7\\ ⇔9x-14x=7-15\\ ⇔-5x=-8\\ ⇔x=\dfrac{-8}{5}=\dfrac85\\ \text{Vậy x = $\dfrac85$}\\ 6)\ \dfrac{2x+3}{6}=\dfrac{7x-3}{15}\\ ⇔15(2x+3)=6(7x-3)\\ ⇔30x+45=42x-18\\ ⇔30x-42x=-18-45\\ ⇔-12x=-63\\ ⇔x=\dfrac{-63}{-12}=\dfrac{21}4\\ \text{Vậy x = $\dfrac{21}4$}\\ 7)\ \dfrac{6x-5}{-7}=\dfrac{5x-3}{-5}\\ ⇔-5(6x-5)=-7(5x-3)\\ ⇔-30x+25=-35x+21\\ ⇔-30x+35x=21-25\\ ⇔5x=-4\\ ⇔x=\dfrac{-4}5\\ \text{Vậy x = $\dfrac{-4}5$}\)
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