1. Решите уравнение:

### 1 а) $\frac{1-4x}{5}=1$ $1-4x=5$ $-4x=4$ $x=-1$ б) $\frac{3x-10}{2}=-1$ $3x-10=-2$ $3x=8$ $x=\frac{8}{3}=2\frac{2}{3}$ в) $\frac{x+3}{10}=\frac{1}{5}$ $x+3 = \frac{10}{5}$ $x+3=2$ $x=-1$ ### 2 а) $\frac{8x+3}{7}=\frac{10x-1}{7}$ $8x+3=10x-1$ $3+1=10x-8x$ $2x=4$ $x=2$ б) $\frac{x+2}{5}=\frac{3x-5}{4}$ $4(x+2)=5(3x-5)$ $4x+8=15x-25$ $8+25=15x-4x$ $33=11x$ $x=3$ в) $\frac{7-x}{6}=\frac{19x-11}{8}$ $8(7-x)=6(19x-11)$ $56-8x=114x-66$ $56+66=114x+8x$ $122=122x$ $x=1$ ### 3 а) $\frac{5x-9}{4}+\frac{5x-7}{4}=1$ $\frac{10x-16}{4}=1$ $10x-16=4$ $10x=20$ $x=2$ б) $2x - \frac{2x+3}{3} = \frac{x-6}{3}$ $6x - (2x+3) = x-6$ $6x-2x-3=x-6$ $4x-3=x-6$ $3x=-3$ $x=-1$ в) $\frac{2-x}{5}-\frac{x}{15}=\frac{1}{3}$ Multiply by 15: $3(2-x) - x = 5$ $6-3x-x=5$ $-4x=-1$ $x=\frac{1}{4}=0,25$ г) $\frac{x}{7}-\frac{3x-1}{14}=2$ Multiply by 14: $2x - (3x-1) = 28$ $2x-3x+1=28$ $-x=27$ $x=-27$ д) $\frac{2x-3}{9}+\frac{x-1}{5}=2$ Multiply by 45: $5(2x-3) + 9(x-1) = 90$ $10x-15+9x-9=90$ $19x-24=90$ $19x=114$ $x=6$ е) $\frac{x+14}{5}-\frac{6x+1}{7}=1$ Multiply by 35: $7(x+14) - 5(6x+1) = 35$ $7x+98-30x-5=35$ $-23x+93=35$ $-23x=-58$ $x=\frac{58}{23}=2\frac{12}{23}$