gọi k là hệ số ty lệ

ta có x/3 = y/4 =   k

18k²+16k^{2 =} 136 => 34k² = 136 => k² =4  =>k=2

x = 2.3 = 6

y = 2.4 = 8

\(a)\) \(2x-5=21\)

\(\Leftrightarrow\) \(2x=21+5\)

\(\Leftrightarrow\) \(2x=26\)

\(\Leftrightarrow\) \(x=26:2\)

\(\Leftrightarrow\) \(=13\)

\(b)\) \(\frac{3}{4}+\frac{1}{4}x=\frac{5}{6}\)

\(\Leftrightarrow\) \(\frac{1}{4}x=\frac{5}{6}-\frac{3}{4}\)

\(\Leftrightarrow\) \(\frac{1}{4}x=\frac{1}{12}\)

\(\Leftrightarrow\) \(x=\frac{1}{3}\)

\(c)\) \(\frac{7}{8}-\frac{1}{2}x=\frac{5}{6}\)

\(\Leftrightarrow\) \(\frac{1}{2}x=\frac{7}{8}-\frac{5}{6}\)

\(\Leftrightarrow\) \(\frac{1}{2}x=\frac{1}{24}\)

\(\Leftrightarrow\) \(x=\frac{1}{12}\)

x+3 chia hết cho x-1

x-1 chia hết cho x-1

=> x+3 - (x-1)=4 chia hết cho x-1

  \(x-1\in\left\{1;-1;2;-2;4;-4\right\}\text{ }\)

=>\(x\in\left\{2;0;3;-1;5;-3\right\}\text{ }\)

b) 2x -1 chia hết cho 2x-1

=> 2(2x-1)=4x-2 chia hết cho 2x-1

=> 4x+3 - (4x-2)=5 chia hết cho 2x-1

\(2x-1\in\left\{1;-1;5;-5\right\}\text{ }\)

=> \(x\in\text{ }\left\{1;0;3;-2\right\}\)

a) x+3=(x-1)+4 vì x-1 đã chia hết cho x-1 rồi => x+3 chia hết cho x-1 <=> 4 chia hết cho x-1 <=> x-1 thuộc Ư(4) <=> x-1 thuộc (1;2;4) => x thuộc (2;3;5)

b) 4x(x-3) =4x(x-1-2)=4x(x-1)-4x.(-2)=4x(x-1)+4x.2

vì...( như trên) =>x-1 phải thuộc Ư(2 <=> x-1 thuộc (1;2) <=> x thuộc(2;3)

`1/2 xx x +3/2 =7`

`=> 1/2 xx x = 7-3/2`

`=> 1/2 xx x = 14/2 -3/2`

`=> 1/2 xx x = 11/2`

`=> x= 11/2 :1/2`

`=> x=11/2 xx2`

`=> x= 22/2`

`=>x=11`

Vậy `x=11`

__

`3/2 xx x -2/7 xx(x-7/2)=18`

`=> 3/2 xx x -2/7x + 1=18`

`=> (3/2 -2/7 )x+ 1 =18`

`=> 17/14 x=18-1`

`=> 17/14x=17`

`=>x=17:17/14`

`=> x=17 xx 14/17`

`=>x=14`

a) \(\dfrac{1}{2}\times x+\dfrac{3}{2}=7\)

\(\dfrac{1}{2}\times x=7-\dfrac{3}{2}\)

\(\dfrac{1}{2}\times x=\dfrac{11}{2}\)

\(x=\dfrac{11}{2}\div\dfrac{1}{2}\\ x=\dfrac{11}{2}\times2\\ x=\dfrac{22}{2}=11\)

b) \(\dfrac{3}{2}\times x-\dfrac{2}{7}\times\left(x-\dfrac{7}{2}\right)=18\)

\(\dfrac{3}{2}\times x-\left(\dfrac{2}{7}x-1\right)=18\)

\(\dfrac{3}{2}\times x-\dfrac{2}{7}x+1=18\)

\(\dfrac{3}{2}x-\dfrac{2}{7}x+1=18\)

\(\dfrac{17}{14}x+1=18\)

\(\dfrac{17}{14}x=18-1\)

\(\dfrac{17}{14}x=17\)

\(x=17\div\dfrac{17}{14}\)

\(x=17\times\dfrac{14}{17}\)

\(x=14\)

a) \(\dfrac{1}{2}\times x+\dfrac{3}{2}=7\)

\(\Leftrightarrow\dfrac{1}{2}\times x=7-\dfrac{3}{2}\)

\(\Leftrightarrow\dfrac{1}{2}\times x=\dfrac{11}{2}\)

\(\Leftrightarrow x=\dfrac{11}{2}:\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{11}{2}\times\dfrac{2}{1}\)

\(\Rightarrow x=11\)

b) \(\dfrac{3}{2}\times x-\dfrac{2}{7}\times\left(x-\dfrac{7}{2}\right)=18\)

\(\Leftrightarrow\dfrac{3}{2}\times x-\dfrac{7}{2}\times x+1=18\)

\(\Leftrightarrow\left(\dfrac{3}{2}-\dfrac{7}{2}\right)\times x+1=18\)

\(\Leftrightarrow\dfrac{17}{14}\times x=18-1\)

\(\Leftrightarrow\dfrac{17}{14}\times x=17\)

\(\Leftrightarrow x=17:\dfrac{17}{14}\)

\(\Leftrightarrow x=17\times\dfrac{14}{17}\)

\(\Rightarrow x=14\)