Question

1)-3 <1+2 x <72)-7 <2x+1<2

Answer 1

Ответ:

Объяснение:

1)

-3<1+2х<7.

{1+2х>-3

{1+2х<7

2х>-4

2х<6

х>-2

х<3

-2<х<3

х∈(-2;3)

2)

-7<2х+1<2

{2х+1>-7

{2х+1<2

{2х>-8

{2х<1

х>-4

х<1/2

-4<х<1/2

х∈(-4;1/2)

Answer 2

To solve the compound inequality $-3 < 1 + 2x < 7$ and $-7 < 2x + 1 < 2$, you can treat each inequality separately and find the solution for each one. Then, you can intersect the solutions to find the common solution.

1. For the first inequality $-3 < 1 + 2x < 7$:

   First, subtract 1 from all parts of the inequality:

   $-3 - 1 < 2x < 7 - 1$

   Simplify:

   $-4 < 2x < 6$

   Now, divide all parts of the inequality by 2:

   $\frac{-4}{2} < \frac{2x}{2} < \frac{6}{2}$

   $-2 < x < 3$

2. For the second inequality $-7 < 2x + 1 < 2$:

   First, subtract 1 from all parts of the inequality:

   $-7 - 1 < 2x + 1 - 1 < 2 - 1$

   Simplify:

   $-8 < 2x < 1$

   Now, divide all parts of the inequality by 2:

   $\frac{-8}{2} < \frac{2x}{2} < \frac{1}{2}$

   $-4 < x < \frac{1}{2}$

Now that you have found the solutions for each inequality separately:

1. $-2 < x < 3$
2. $-4 < x < \frac{1}{2}$

To find the common solution, you can take the intersection of these two intervals. The common solution is the range of values that satisfies both inequalities:

The intersection of $-2 < x < 3$ and $-4 < x < \frac{1}{2}$ is $-2 < x < \frac{1}{2}$.

So, the solution to the compound inequality is:

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