Задание 6. Найдите корень уравнения. 1) x+x/9=10/3; 2) x-x/7=6; 3) x+x/5=12/5 4) x-x/12=11/3 5) x+x/2=-9; 6) x-x/11=50/11 7) 6+x/2=x+3/5; 8) -4+x/5=x+4/2; 9) 1+x/5=x+9/7 Задание 7. Найдите корень уравнения. 1) 4x+7/3+2=7x/2; 2) 6x+8/2+5=5x/3; 3) 9x+6/7+3=7x/6 Задание 8. Найдите корень уравнения. 1) 12/(x+5)=12/5; 2) 6/(x+8)=3/4; 3) 1/(x+2)=1/2 4) 10/x=5/7; 7) 7/(x-5)=2; 8) 4/(x-4)=-5; 9) 11/(x-9)=-10; 10) 7/x=-1 13) 3/(x-19)=19/(x-3); 14) 13/(x-5)=5/(x-13); 15) 6/(x-8)=8/(x-6)

Задание 6. Найдите корень уравнения.

1. 1) \( x + \frac{x}{9} = \frac{10}{3} \)\[ \frac{9x + x}{9} = \frac{10}{3} \]\[ \frac{10x}{9} = \frac{10}{3} \]\[ 10x = \frac{10 \cdot 9}{3} \]\[ 10x = 30 \]\[ x = 3 \]
2. 2) \( x - \frac{x}{7} = 6 \)\[ \frac{7x - x}{7} = 6 \]\[ \frac{6x}{7} = 6 \]\[ 6x = 6 \cdot 7 \]\[ 6x = 42 \]\[ x = 7 \]
3. 3) \( x + \frac{x}{5} = \frac{12}{5} \)\[ \frac{5x + x}{5} = \frac{12}{5} \]\[ \frac{6x}{5} = \frac{12}{5} \]\[ 6x = 12 \]\[ x = 2 \]
4. 4) \( x - \frac{x}{12} = \frac{11}{3} \)\[ \frac{12x - x}{12} = \frac{11}{3} \]\[ \frac{11x}{12} = \frac{11}{3} \]\[ 11x = \frac{11 \cdot 12}{3} \]\[ 11x = 44 \]\[ x = 4 \]
5. 5) \( x + \frac{x}{2} = -9 \)\[ \frac{2x + x}{2} = -9 \]\[ \frac{3x}{2} = -9 \]\[ 3x = -18 \]\[ x = -6 \]
6. 6) \( x - \frac{x}{11} = \frac{50}{11} \)\[ \frac{11x - x}{11} = \frac{50}{11} \]\[ \frac{10x}{11} = \frac{50}{11} \]\[ 10x = 50 \]\[ x = 5 \]
7. 7) \( 6 + \frac{x}{2} = \frac{x + 3}{5} \)\[ \frac{12 \cdot 5 + 5x}{10} = \frac{2 \cdot (x + 3)}{10} \]\[ 60 + 5x = 2x + 6 \]\[ 3x = -54 \]\[ x = -18 \]
8. 8) \( -4 + \frac{x}{5} = \frac{x + 4}{2} \)\[ \frac{-4 \cdot 5 + x}{5} = \frac{x + 4}{2} \]\[ \frac{-20 + x}{5} = \frac{x + 4}{2} \]\[ 2(-20 + x) = 5(x + 4) \]\[ -40 + 2x = 5x + 20 \]\[ -3x = 60 \]\[ x = -20 \]
9. 9) \( 1 + \frac{x}{5} = \frac{x + 9}{7} \)\[ \frac{5 + x}{5} = \frac{x + 9}{7} \]\[ 7(5 + x) = 5(x + 9) \]\[ 35 + 7x = 5x + 45 \]\[ 2x = 10 \]\[ x = 5 \]

Задание 7. Найдите корень уравнения.

1. 1) \( \frac{4x + 7}{3} + 2 = \frac{7x}{2} \)\[ \frac{4x + 7 + 6}{3} = \frac{7x}{2} \]\[ \frac{4x + 13}{3} = \frac{7x}{2} \]\[ 2(4x + 13) = 3(7x) \]\[ 8x + 26 = 21x \]\[ 13x = 26 \]\[ x = 2 \]
2. 2) \( \frac{6x + 8}{2} + 5 = \frac{5x}{3} \)\[ \frac{6x + 8 + 10}{2} = \frac{5x}{3} \]\[ \frac{6x + 18}{2} = \frac{5x}{3} \]\[ 3(6x + 18) = 2(5x) \]\[ 18x + 54 = 10x \]\[ 8x = -54 \]\[ x = -\frac{27}{4} = -6.75 \]
3. 3) \( \frac{9x + 6}{7} + 3 = \frac{7x}{6} \)\[ \frac{9x + 6 + 21}{7} = \frac{7x}{6} \]\[ \frac{9x + 27}{7} = \frac{7x}{6} \]\[ 6(9x + 27) = 7(7x) \]\[ 54x + 162 = 49x \]\[ 5x = -162 \]\[ x = -\frac{162}{5} = -32.4 \]

Задание 8. Найдите корень уравнения.

1. 1) \( \frac{12}{x + 5} = \frac{12}{5} \)\[ x + 5 = 5 \]\[ x = 0 \]
2. 2) \( \frac{6}{x + 8} = \frac{3}{4} \)\[ 3(x + 8) = 6 \cdot 4 \]\[ 3x + 24 = 24 \]\[ 3x = 0 \]\[ x = 0 \]
3. 3) \( \frac{1}{x + 2} = \frac{1}{2} \)\[ x + 2 = 2 \]\[ x = 0 \]
4. 4) \( \frac{10}{x} = \frac{5}{7} \)\[ 5x = 10 \cdot 7 \]\[ 5x = 70 \]\[ x = 14 \]
5. 7) \( \frac{7}{x - 5} = 2 \)\[ 2(x - 5) = 7 \]\[ 2x - 10 = 7 \]\[ 2x = 17 \]\[ x = \frac{17}{2} = 8.5 \]
6. 8) \( \frac{4}{x - 4} = -5 \)\[ -5(x - 4) = 4 \]\[ -5x + 20 = 4 \]\[ -5x = -16 \]\[ x = \frac{16}{5} = 3.2 \]
7. 9) \( \frac{11}{x - 9} = -10 \)\[ -10(x - 9) = 11 \]\[ -10x + 90 = 11 \]\[ -10x = -79 \]\[ x = \frac{79}{10} = 7.9 \]
8. 10) \( \frac{7}{x} = -1 \)\[ -x = 7 \]\[ x = -7 \]
9. 13) \( \frac{3}{x - 19} = \frac{19}{x - 3} \)\[ 3(x - 3) = 19(x - 19) \]\[ 3x - 9 = 19x - 361 \]\[ -16x = -352 \]\[ x = 22 \]
10. 14) \( \frac{13}{x - 5} = \frac{5}{x - 13} \)\[ 13(x - 13) = 5(x - 5) \]\[ 13x - 169 = 5x - 25 \]\[ 8x = 144 \]\[ x = 18 \]
11. 15) \( \frac{6}{x - 8} = \frac{8}{x - 6} \)\[ 6(x - 6) = 8(x - 8) \]\[ 6x - 36 = 8x - 64 \]\[ -2x = -28 \]\[ x = 14 \]