Question

3 4/5х-13/21<8х+1/3+3 101/105​

Answer 1

$3 \frac{4}{5} x - \frac{13}{21} < 8x + \frac{1}{3} + 3 \frac{101}{105} \\ \frac{19}{5} x - \frac{13}{21} < 8x + \frac{1}{3} + \frac{416}{105} \\ \frac{19}{5} x - \frac{13}{21} < 8x + \frac{451}{105} \\ 399x - 65 < 840x + 451 \\ 399x - 840x < 451 + 65 \\ - 441x < 516 \\ x > - \frac{172}{147}$

Answer 2

To solve the inequality $\frac{3}{5}x - \frac{13}{21} < 8x + \frac{1}{3} + \frac{3}{101/105},$ you can follow these steps:

1. First, simplify the expression on the right side:

$\frac{3}{5}x - \frac{13}{21} < 8x + \frac{1}{3} + \frac{3}{101/105}$

$\frac{3}{5}x - \frac{13}{21} < 8x + \frac{1}{3} + \frac{3}{101/105}$

$\frac{3}{5}x - \frac{13}{21} < 8x + \frac{1}{3} + \frac{315}{101}$

2. Combine like terms on both sides of the inequality:

$\frac{3}{5}x - \frac{13}{21} - 8x - \frac{1}{3} - \frac{315}{101} < 0$

3. Now, you can simplify the left side of the inequality by finding a common denominator:

$\frac{63}{105}x - \frac{55}{105} - \frac{504}{105}x - \frac{35}{105} - \frac{315}{101} < 0$

4. Combine the fractions on the left side:

$\frac{63x - 55 - 504x - 35 - 315}{105} < 0$

5. Simplify the expression:

$\frac{-441x - 405}{105} < 0$

6. Further simplify the expression:

$\frac{-7(63x + 45)}{105} < 0$

7. Divide both sides by -7, which is a negative number, so the inequality sign will flip:

$\frac{63x + 45}{105} > 0$

8. Reduce the fraction:

$\frac{3(21x + 15)}{5(21)} > 0$

$\frac{3(21x + 15)}{105} > 0$

9. Now, you have:

$\frac{3(21x + 15)}{105} > 0$

10. Divide both sides by 3:

$\frac{21x + 15}{35} > 0$

11. Finally, solve for $x$:

$\frac{21x + 15}{35} > 0$

To find the solution for $x$, you need to consider when the expression on the left is greater than zero. The numerator, $21x + 15$, is greater than zero when $21x > -15$, which is satisfied when $x > -15/21$. Therefore, the solution to the inequality is:

$x > -\frac{5}{7}$

So, the solution set for the inequality is $x > -\frac{5}{7}$.