Resolver las siguientes ecuaciones: 1. x/6 + 5 = 1/3 - x 2. 3x/5 - 2x/3 + 1/5 = 0 3. 1/(2x) + 1/4 = 1/(10x) + 1/5 4. x/2 + 2 - x/12 = x/6 - 5/4 5. (3x)/4 - 1/5 + 2x = 5/4 - (3x)/20... Resolver las siguientes ecuaciones: 1. x/6 + 5 = 1/3 - x 2. 3x/5 - 2x/3 + 1/5 = 0 3. 1/(2x) + 1/4 = 1/(10x) + 1/5 4. x/2 + 2 - x/12 = x/6 - 5/4 5. (3x)/4 - 1/5 + 2x = 5/4 - (3x)/20 6. 2/(3x) - 5/x = 7/10 - 3/(2x) + 1 7. (x-4)/3 - 5 = 0 8. x - (x+2)/12 = (5x)/2 9. x - (5x-1)/3 = 4x - 3/5 10. 10x - (8x-3)/4 = 2(x-3) Read more

Steps to Solve

1. Solve equation 1: $\frac{x}{6} + 5 = \frac{1}{3} - x$

Add $x$ to both sides: $\frac{x}{6} + x + 5 = \frac{1}{3}$ $\frac{7x}{6} + 5 = \frac{1}{3}$

Subtract 5 from both sides: $\frac{7x}{6} = \frac{1}{3} - 5$ $\frac{7x}{6} = \frac{1}{3} - \frac{15}{3}$ $\frac{7x}{6} = -\frac{14}{3}$

Multiply both sides by $\frac{6}{7}$: $x = -\frac{14}{3} \cdot \frac{6}{7}$ $x = -\frac{2 \cdot 2}{1}$ $x = -4$

2. Solve equation 2: $\frac{3x}{5} - \frac{2x}{3} + \frac{1}{5} = 0$

Multiply both sides by 15 (the least common multiple of 5 and 3): $15(\frac{3x}{5} - \frac{2x}{3} + \frac{1}{5}) = 15(0)$ $9x - 10x + 3 = 0$ $-x + 3 = 0$

Add $x$ to both sides: $3 = x$ $x = 3$

3. Solve equation 3: $\frac{1}{2x} + \frac{1}{4} = \frac{1}{10x} + \frac{1}{5}$

Subtract $\frac{1}{10x}$ from both sides: $\frac{1}{2x} - \frac{1}{10x} + \frac{1}{4} = \frac{1}{5}$ $\frac{5}{10x} - \frac{1}{10x} + \frac{1}{4} = \frac{1}{5}$ $\frac{4}{10x} + \frac{1}{4} = \frac{1}{5}$ $\frac{2}{5x} = \frac{1}{5} - \frac{1}{4} = \frac{4}{20} - \frac{5}{20} = -\frac{1}{20}$

$\frac{2}{5x} = -\frac{1}{20}$ Cross multiply: $-5x = 40$

Divide by -5: $x = -8$

4. Solve equation 4: $\frac{x}{2} + 2 - \frac{x}{12} = \frac{x}{6} - \frac{5}{4}$

Multiply both sides by 12: $12(\frac{x}{2} + 2 - \frac{x}{12}) = 12(\frac{x}{6} - \frac{5}{4})$ $6x + 24 - x = 2x - 15$ $5x + 24 = 2x - 15$

Subtract $2x$ from both sides: $3x + 24 = -15$

Subtract 24 from both sides: $3x = -39$

Divide by 3: $x = -13$

5. Solve equation 5: $\frac{3x}{4} - \frac{1}{5} + 2x = \frac{5}{4} - \frac{3x}{20}$

Multiply both sides by 20: $20(\frac{3x}{4} - \frac{1}{5} + 2x) = 20(\frac{5}{4} - \frac{3x}{20})$ $15x - 4 + 40x = 25 - 3x$ $55x - 4 = 25 - 3x$

Add $3x$ to both sides: $58x - 4 = 25$

Add 4 to both sides: $58x = 29$

Divide by 58: $x = \frac{29}{58} = \frac{1}{2}$

6. Solve equation 6: $\frac{2}{3x} - \frac{5}{x} = \frac{7}{10} - \frac{3}{2x} + 1$

Multiply both sides by $30x$: $30x(\frac{2}{3x} - \frac{5}{x}) = 30x(\frac{7}{10} - \frac{3}{2x} + 1)$ $20 - 150 = 21x - 45 + 30x$ $-130 = 51x - 45$

Add 45 to both sides: $-85 = 51x$

Divide by 51: $x = -\frac{85}{51} = -\frac{5 \cdot 17}{3 \cdot 17} = -\frac{5}{3}$

7. Solve equation 7: $\frac{x-4}{3} - 5 = 0$

Add 5 to both sides: $\frac{x-4}{3} = 5$

Multiply by 3: $x - 4 = 15$

Add 4 to both sides: $x = 19$

8. Solve equation 8: $x - \frac{x+2}{12} = \frac{5x}{2}$

Multiply both sides by 12: $12(x - \frac{x+2}{12}) = 12(\frac{5x}{2})$ $12x - (x+2) = 30x$ $12x - x - 2 = 30x$ $11x - 2 = 30x$

Subtract $11x$ from both sides: $-2 = 19x$

Divide by 19: $x = -\frac{2}{19}$

9. Solve equation 9: $x - \frac{5x-1}{3} = 4x - \frac{3}{5}$

Multiply both sides by 15: $15(x - \frac{5x-1}{3}) = 15(4x - \frac{3}{5})$ $15x - 5(5x-1) = 60x - 9$ $15x - 25x + 5 = 60x - 9$ $-10x + 5 = 60x - 9$

Add $10x$ to both sides: $5 = 70x - 9$

Add 9 to both sides: $14 = 70x$

Divide by 70: $x = \frac{14}{70} = \frac{1}{5}$

10. Solve equation 10: $10x - \frac{8x-3}{4} = 2(x-3)$

Multiply both sides by 4: $4(10x - \frac{8x-3}{4}) = 4(2(x-3))$ $40x - (8x-3) = 8(x-3)$ $40x - 8x + 3 = 8x - 24$ $32x + 3 = 8x - 24$

Subtract $8x$ from both sides: $24x + 3 = -24$

Subtract 3 from both sides: $24x = -27$

Divide by 24: $x = -\frac{27}{24} = -\frac{9}{8}$