Question

7 х - 21 < 0,1 - x > 0;​

Answer 1

Пошаговое объяснение:

1)7х - 21 < 0

7х < 21

х < 3

х є (-∞; 3] - (квадратная скобка обязательна)

2) 1 - х > 0

-х > - 1

х > 1

х є [1;∞)

Answer 2

To solve this system of inequalities:

1. $7x - 21 < 0$
2. $1 - x > 0$

Let's solve each inequality separately:

1. $7x - 21 < 0$

First, add 21 to both sides of the inequality:

$7x - 21 + 21 < 0 + 21$

This simplifies to:

$7x < 21$

Now, divide both sides by 7 to isolate x:

$\frac{7x}{7} < \frac{21}{7}$

$x < 3$

So, the solution to the first inequality is $x < 3$.

2. $1 - x > 0$

First, subtract 1 from both sides of the inequality:

$1 - x - 1 > 0 - 1$

Simplify:

$-x > -1$

Now, multiply both sides by -1. Remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality sign:

$-1 \cdot (-x) < -1 \cdot (-1)$

This simplifies to:

$x < 1$

So, the solution to the second inequality is $x < 1$.

Now, to find the solution to the system of inequalities, you need to find the values of x that satisfy both $x < 3$ and $x < 1$. Since $x$ must be less than both 3 and 1, the solution is the intersection of these two sets, which means $x$ must be less than the smaller of the two values, which is 1.

So, the solution to the system of inequalities is $x < 1$.