Đáp án:

 

Giải thích các bước giải:

 

Đáp án:

$5)$ 

$a) 5x-3.(x-2)=x+17$

$⇔ 5x-3x+6-x-17=0$

$⇔ (5x-3x-x)+(6-17)=0$

$⇔ x-11=0$

$⇔ x=11$

$\text{Vậy S={11}}$

$\text{_____________________________}$

$b) -18-3.(x+4)=2.(x-7)+13$

$⇔ -18-3x-12=2x-14+13$

$⇔ -3x-30-2x+1=0$

$⇔ -5x-29=0$

$⇔ -5x=29$

$⇔ x= -5,8$

$\text{Vậy S={-5,8}}$

$\text{_____________________________}$

$c) (3x-5)²-(3x+5)²=58$

$⇔ (3x-5-3x-5).(3x-5+3x+5)=58$

$⇔ -10.6x=58$

$⇔ -60x=58$

$⇔ x= -\dfrac{29}{30}$

$\text{Vậy S=}$ $\left\{-{\dfrac{{29}}{{30}}}\right\}$

$\text{_____________________________}$

$d) 2.(x+4)-35=5.(x-2)+49$

$⇔ 2x+8-35=5x-10+49$

$⇔ 2x-27-5x-39=0$

$⇔ (2x-5x)-(27+39)=0$

$⇔ -3x-66=0$

$⇔ -3x=66$

$⇔ x= -22$

$\text{Vậy S={-22}}$

$\text{_____________________________}$

$6)$

$a) (x-5)²-(x+5)²=-20.(x+7)$

$⇔ (x-5-x-5).(x-5+x+5)= -20x-140$

$⇔ -10.2x=-20x-140$

$⇔ -20x+20x+140=0$

$⇔ 0x+140=0$

$⇔ 0x=-140$ $\text{(Vô lí)}$

$\text{Vậy S={Ф}}$   $\text{(Ф :tập hợp rỗng)}$

$\text{_____________________________}$

$b) 2x-31=2.(x+3)-37$

$⇔ 2x-31= 2x+6-37$

$⇔ 2x-31-2x+31=0$

$⇔ 0x+0=0$

$⇔ 0x=0$

$\text{Vậy S vô số nghiệm}$

$\text{_____________________________}$

 $7)$

$a) \dfrac{3x-2}{3}+\dfrac{1}{5}=\dfrac{x+4}{15}$

$⇔ \dfrac{5.(3x-2)}{15}+\dfrac{3}{15}=\dfrac{x+4}{15}$

$⇒ 15x-10+3=x+4$

$⇔ 15x-7-x-4=0$

$⇔ (15-x)-(7+4)=0$

$⇔ 14x-11=0$

$⇔ 14x=11$

$⇔ x= \dfrac{11}{14}$

$\text{Vậy S=}$ $\left\{{\dfrac{{11}}{{14}}}\right\}$

$\text{_____________________________}$

$b) \dfrac{5x+2}{7}+\dfrac{2}{5}= \dfrac{x-2}{35}$

$⇔ \dfrac{5.(5x+2)}{35}+\dfrac{14}{35}=\dfrac{x-2}{35}$

$⇒ 25x+10+14=x-2$

$⇔ 25x+24-x+2=-$

$⇔ 24x+26=0$

$⇔ 24x=-26$

$⇔ x=- \dfrac{13}{12}$

$\text{Vậy S=}$ $\left\{-{\dfrac{{13}}{{12}}}\right\}$

$\text{_____________________________}$

$c) \dfrac{x+3}{5}+3=\dfrac{x-4}{3}$

$⇔ \dfrac{3.(x+3)}{15}+\dfrac{45}{15}= \dfrac{5.(x-4)}{15}$

$⇒ 3x+9+45= 5x-20$

$⇔ 3x+54-5x+20=0$

$⇔ -2x+74=0$

$⇔ -2x=-74$

$⇔ x=37$

$\text{Vậy S={37}}$

$\text{_____________________________}$