Question

9772)х-х+3/2>1,-х/2<2-х/3​

Answer 1

Ответ:

2) Система неравенств:

x -(x+3)/2≥1; 2x-x-3≥2; x≥2+3; x≥5

-x/2≤2 -x/3; (2x-3x)/2≥2; x≥4

x∈[5; +∞)

3) Система неравенств:

x/3 -x/4<x/6 -1; (4x-3x)/12<(2x-12)/12; x<2x-12; 2x-x>12; x>12

6 -x/2>x/4 +3; (24-2x)/4>(x+12)/4; 2x+x<24-12; x<12/3; x<4

Данная система неравенств не имеет решений.

4) Система неравенств:

x/5 -2/3<2/5 -x/3; (3x-10)/15<(6-5x)/15; 3x+5x<10+6; x<16/8; x<2

2/7 +x/3>x/7 -2/3; (6+7x)/21>(3x-14)/21; 3x-7x>6+14; x>20/(-4); x>-5

x∈(-5; 2)

Answer 2

Let's solve the inequalities step by step:

1. $9772x - x + \frac{3}{2} > 1$:

   Combine like terms on the left side:

   $9771x + \frac{3}{2} > 1$

   Subtract $\frac{3}{2}$ from both sides:

   $9771x > 1 - \frac{3}{2}$

   $9771x > \frac{2}{2} - \frac{3}{2}$

   $9771x > -\frac{1}{2}$

   Now, divide both sides by 9771 to isolate $x$:

   $x > \frac{-1}{2 \cdot 9771}$

   $x > -\frac{1}{19542}$

2. $-\frac{x}{2} < 2 - \frac{x}{3}$:

   To simplify this inequality, let's first clear fractions by multiplying both sides by the common denominator, which is 6:

   $-3x < 12 - 2x$

   Now, add $2x$ to both sides to get $x$ terms on one side:

   $-3x + 2x < 12$

   $-x < 12$

   To isolate $x$, multiply both sides by -1. When you multiply an inequality by a negative number, the direction of the inequality sign flips:

   $x > -12$

So, the solutions to the inequalities are:

1. $x > -\frac{1}{19542}$
2. $x > -12$