Question

17 x – 21 <0; 1) (1 – x > 0;20 x + 40 >0) 2 - 4 x > 0;​

Answer 1

Пошаговое объяснение:

$1)17x - 21 < 0 \\ 17x < 21 \\ x < \frac{21}{17} \\ \\ 2)1 - x > 0 \\ - x > - 1 \\ x - < 1 \\ \\ 3)20x + 40 > 0 \\ 20x > - 40 \\ x > - 2 \\ \\ 4)2 - 4x > 0 \\ - 4x > - 2 \\ x < \frac{1}{2}$

Answer 2

Let's solve the given inequalities step by step:

1. $17x - 21 < 0$

   To solve this inequality, we'll first isolate $x$ by adding $21$ to both sides:

   $17x < 21$

   Now, divide both sides by $17$:

   $x < \frac{21}{17}$

2. $1 - x > 0$

   To solve this inequality, isolate $x$ by subtracting $1$ from both sides:

   $-x > -1$

   Now, multiply both sides by $-1$ (which reverses the inequality):

   $x < 1$

3. $20x + 40 > 0$

   To solve this inequality, isolate $x$ by subtracting $40$ from both sides:

   $20x > -40$

   Now, divide both sides by $20$:

   $x > -2$

4. $2 - 4x > 0$

   To solve this inequality, isolate $x$ by subtracting $2$ from both sides:

   $-4x > -2$

   Now, divide both sides by $-4$ (which reverses the inequality):

   $x < \frac{1}{2}$

Combining the solutions:

• From the first inequality, $x < \frac{21}{17}$
• From the second inequality, $x < 1$
• From the third inequality, $x > -2$
• From the fourth inequality, $x < \frac{1}{2}$

To find the overall solution that satisfies all these conditions, we take the intersection of these intervals:

$x \in \left(-2, \frac{21}{17}\right) \cap \left(-\infty, 1\right) \cap \left(-\infty, \frac{1}{2}\right)$

The final solution is $x \in \left(-2, \frac{21}{17}\right)$.