Tìm x: (3.x + 11) – 17 = 30

a, x - 108 × 42 = 2378

=> x - 4536 = 2378

=> x = 6914

vậy_

b,1337 + 13 × x = 6745

=> 10 × x = 5408

=> x = 540,8

vậy_

c, x × 10 + 16 × x = 972

=> x × (10 + 16) = 972

=> x× 26 = 972

=> x = \(\frac{486}{13}\)

vậy_

d, 25 × x - x  = 59904 : 32

=> x × (25 - 1) = 1872

=> x × 24 = 1872

=> x = 78

vậy_

\(x-108.42=2378\)

\(x-4536=2378\)

\(x=6914\)

\(a,1337+13\times x=6745\\ \Rightarrow13\times x=6745-1337\\ \Rightarrow x=5408:13\\ \Rightarrow x=416\\ b,142\times x-41\times x-x=408000\\ \Rightarrow x\times\left(142-41-1\right)=408000\\ \Rightarrow x\times100=408000\\ \Rightarrow x=408000:100\\ \Rightarrow x=4080\)

a.      1337 + 13 x x = 6745  

          13 x x            = 6745-1337

           13 x x           = 5408

                     x         = 5408 : 13

                     x         = 416

 b. 142 x x – 41 x x – x = 408000

142 x x – 41 x x – x x 1 = 408000

(142-41-1) x x               = 408 000

100 x x                          = 408000

                x                    = 408 000:100

             x                       = 4080

a) X nhân 3/8 = 9/16
    X= 9/16 chia 3/8
    X= 9/16 nhân 8/3
    X= 3/2
b) x chia 12/7=5/8
    x= 5/8 nhân 12/7
    x= 15/14

Lời giải:

a. 

$x\times \frac{3}{8}=\frac{9}{16}$

$x=\frac{9}{16}: \frac{3}{8}$

$x=\frac{3}{2}$

b.

$x:\frac{12}{7}=\frac{5}{8}$

$x=\frac{5}{8}\times \frac{12}{7}$

$x=\frac{15}{14}$

a) x : 4 = 8

x = 8 × 4

x = 32

b) 4 × x = 12 + 8

4 × x = 20

x = 20 : 4

x = 5

c) 30 : x = 14 + 16

30 : x = 30

x = 30 : 30

x = 1

a.\(\left(-12\right)x-14=-2\)

\(\left(-12\right)x=-2+14\)

\(\left(-12\right)x=12\)

\(x=12:\left(-12\right)\)

\(x=-1\)

\(b,\left(-8\right)x=\left(-5\right)\left(-7\right)-3\)

\(\left(-8\right)x=35-3\)

\(\left(-8\right)x=32\)

\(x=32:\left(-8\right)\)

\(x=-4\)

\(c,\left(-9\right)x+3=\left(-2\right)\left(-7\right)+16\)

\(\left(-9\right)x+3=14+16\)

\(\left(-9\right)x+3=30\)

\(\left(-9\right)x=30-3\)

\(\left(-9\right)x=27\)

\(x=27:\left(-9\right)\)

\(x=-3\)

a) \(\dfrac{2x+5}{2x+1}=\dfrac{2x+1+4}{2x+1}=\dfrac{2x+1}{2x+1}+\dfrac{4}{2x+1}=1+\dfrac{4}{2x+1}\)  

Để \(\dfrac{2x+5}{2x+1}\in Z\) thì \(\dfrac{4}{2x+1}\in Z\) 

\(\Rightarrow4\) ⋮ \(2x+1\)

\(\Rightarrow2x+1\inƯ\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

\(\Rightarrow2x\in\left\{0;-2;1;-3;3;-5\right\}\)

\(\Rightarrow x\in\left\{0;-1;\dfrac{1}{2};-\dfrac{3}{2};\dfrac{3}{2};-\dfrac{5}{2}\right\}\)

Mà x nguyên \(\Rightarrow\text{x}\in\left\{0;-1\right\}\) 

b) \(\dfrac{3x+5}{x+1}=\dfrac{3x+3+2}{x+1}=\dfrac{3\left(x+1\right)+2}{x+1}=\dfrac{3\left(x+1\right)}{x+1}+\dfrac{2}{x+1}=3+\dfrac{2}{x+1}\) 

Để \(\dfrac{3x+5}{x+1}\in Z\) thì \(\dfrac{2}{x+1}\in Z\) 

\(\Rightarrow2\) ⋮ \(x+1\)

\(\Rightarrow x+1\inƯ\left(2\right)=\left\{1;-1;2;-2\right\}\)

\(\Rightarrow x\in\left\{0;-2;1;-3\right\}\) 

c) \(\dfrac{3x+8}{x-1}=\dfrac{3x-3+11}{x-1}=\dfrac{3\left(x-1\right)+11}{x-1}=\dfrac{3\left(x-1\right)}{x-1}+\dfrac{11}{x-1}=3+\dfrac{11}{x-1}\)  

Để: \(\dfrac{3x+8}{x-1}\in Z\) thì \(\dfrac{11}{x-1}\in Z\)

\(\Rightarrow11\) ⋮ \(x-1\)

\(\Rightarrow x-1\inƯ\left(11\right)=\left\{1;-1;11;-11\right\}\)

\(\Rightarrow x\in\left\{2;0;12;-10\right\}\)

d) \(\dfrac{5x+12}{x-2}=\dfrac{5x-10+22}{x-2}=\dfrac{5\left(x-2\right)+22}{x-2}=\dfrac{5\left(x-2\right)}{x-2}+\dfrac{22}{x-2}=5+\dfrac{22}{x-2}\)

Để: \(\dfrac{5x+12}{x-2}\in Z\) thì \(\dfrac{22}{x-2}\in Z\)

\(\Rightarrow22\) ⋮ \(x-2\)

\(\Rightarrow x-2\inƯ\left(22\right)=\left\{1;-1;2;-2;11;-11;22;-22\right\}\)

\(\Rightarrow x\in\left\{3;1;4;0;13;-9;24;-20\right\}\)

e) \(\dfrac{7x-12}{x+16}=\dfrac{7x+112-124}{x+16}=\dfrac{7\left(x+16\right)-124}{x+16}=\dfrac{7\left(x+16\right)}{x+16}-\dfrac{124}{x+16}=7-\dfrac{124}{x+16}\)

Để \(\dfrac{7x-12}{x+16}\in Z\) thì \(\dfrac{124}{x+16}\in Z\) 

\(\Rightarrow124\) ⋮ \(x+16\)

\(\Rightarrow x+16\inƯ\left(124\right)=\left\{1;-1;2;-2;4;-4;31;-31;62;-62;124;-124\right\}\)

\(\Rightarrow x\in\left\{-15;-17;-14;-18;-12;-20;15;-47;46;-78;108;-140\right\}\)