e) \(3a+15⋮3a-1\)

=> \(3a-1+16⋮3a-1\)

Mà \(3a-1⋮3a-1\)

=> \(16⋮3a-1\)

.............

a) \(a+11⋮a+3\)

\(\Rightarrow\left(a+3\right)+8⋮a+3\)

Mà \(a+3⋮a+3\)

=> \(8⋮a+3\)

=> \(a+3\in\text{Ư}\left(8\right)=\left\{\text{ }\pm1;\pm2\pm4;\pm8\right\}\)

=> \(a\in\left\{-4;-2;-5;-1;-7;1;-11;5\right\}\)

b) \(a-3⋮a-14\)

=> \(\left(a-14\right)+11⋮a-14\)

Mà \(a-14⋮a-14\)

=> \(11⋮a-14\)

Đến đây bạn tự làm tiếp nhé!

a, 10 ⋮ 3a+1 => 3a+1 ∈ Ư(10) => 3a+1 ∈ {1;2;5;10} => a ∈ { 0 ; 1 3 ; 4 3 ; 3 }. Vì a ∈ N, a ∈ {0;3}

b, a+6 ⋮ a+1 => a+1+5 ⋮ a+1 => 5 ⋮ a+1 => a+1 ∈ Ư(5) =>  a+1 ∈ {1;5} => a ∈ {0;4}

c, 3a+7 ⋮ 2a+3 => 2.(3a+7) - 3(2a+3) ⋮ 2a+3 => 5 ⋮ 2a+3 => 2a+3 ∈ Ư(5)

=> 2a+3 ∈ {1;5} => a = 1

d, 6a+11 ⋮ 2a+3 => 3.(2a+3)+2 ⋮ 2a+3 => 2 ⋮ 2a+3 => 2a+3 ∈ Ư(2)

=> 2a+3 ∈ {1;2} => a ∈ ∅

X Thuộc Z nha

a) \(x+15=18-\left(-27\right)\)

\(\Leftrightarrow x+15=18+27\)

\(\Leftrightarrow x+15=45\)

\(\Leftrightarrow x=45-15\)

\(\Leftrightarrow x=30\)

b) \(-x+7=28\)

\(\Leftrightarrow-x=28-7\)

\(\Leftrightarrow-x=21\)

\(\Leftrightarrow x=-21\)

c) \(20-\left(-x\right)=14\)

\(\Leftrightarrow20+x=14\)

\(\Leftrightarrow x=14-20\)

\(\Leftrightarrow x=-6\)

d) \(2x+5=x-14\)

\(\Leftrightarrow2x+5-\left(x-14\right)=0\)

\(\Leftrightarrow2x+5-x+14=0\)

\(\Leftrightarrow x+19=0\)

\(\Leftrightarrow x=0-19\)

\(\Leftrightarrow x=-19\)

e) \(x+17=-8-20\)

\(\Leftrightarrow x+17=-\left(8+20\right)\)

\(\Leftrightarrow x+17=-28\)

\(\Leftrightarrow x=-28-17\)

\(\Leftrightarrow x=-\left(28+17\right)\)

\(\Leftrightarrow x=-45\)

f) \(3x+15=2x+6\)

\(\Leftrightarrow3x+15-\left(2x+6\right)=0\)

\(\Leftrightarrow3x+15-2x-6=0\)

\(\Leftrightarrow x+9=0\)

\(\Leftrightarrow x=0-9\)

\(\Leftrightarrow x=-9\)

2,

a.\(\left|a+3\right|=\left|-5\right|\)

\(a+3=5\)

\(a=2\)

Vậy a=2

b.\(\left|a-1\right|=2+\left|-3\right|\)

\(a-1=2+3\)

\(a-1=5\)

\(a=6\)

Vậy a=6