Question

7+2x_> 5+x3x+2_<8+x​

Answer 1

Ответ:

Пошаговое объяснение:

Если это система неравенств и выглядит так:

7+2x≥5+x; x-2x≤7-5; -x≤2; x≥-2

3x+2≤8+x; 3x-x≤8-2; 2x≤6; x≤6/2; x≤3

x∈[-2; 3],

а если выглядит так:

7+2x>5+x; x>-2

3x+2<8+x; x<3

x∈(-2; 3).

А если эта не система, а отдельные неравенства, тогда так:

7+2x≥5+x; x-2x≤7-5; -x≤2; x≥-2; x∈[-2; +∞)

7+2x>5+x; x>-2; x∈(-2; +∞)

3x+2≤8+x; 3x-x≤8-2; 2x≤6; x≤6/2; x≤3; x∈(-∞; 3]

3x+2<8+x; x<3; x∈(-∞; -3)

Answer 2

It seems like you've written an inequality expression with variables. Let's simplify and solve it step by step:

7 + 2x > 5 + x3x + 2 < 8 + x

First, let's isolate the terms containing "x" on one side of the inequality:

2x - x3x > 8 - 7 - 5 + 2

Now, let's combine like terms on both sides:

2x - 3x^2 > -2

Next, rearrange the terms to bring them to one side of the inequality:

-3x^2 + 2x > -2

Now, we have a quadratic inequality. To solve this inequality, we need to find the values of "x" that satisfy it.

Let's solve it step by step:

1. First, factor out the common term "x" from the left side:

x(-3x + 2) > -2

2. Now, divide both sides by the factor (-3x + 2). Note that when dividing by a negative number, we need to reverse the direction of the inequality:

x < -2 / (-3x + 2)

3. We also need to consider the possibility that (-3x + 2) might be negative, which would require us to reverse the direction of the inequality again. So, we'll find the critical point where (-3x + 2) equals zero:

-3x + 2 = 0 -3x = -2 x = 2/3

Now, we have two cases to consider:

Case 1: (-3x + 2) > 0 (i.e., when x < 2/3)

In this case, the direction of the inequality remains as it is:

x < -2 / (-3x + 2)

Case 2: (-3x + 2) < 0 (i.e., when x > 2/3)

In this case, we need to reverse the direction of the inequality:

x > -2 / (-3x + 2)

So, the solution to the inequality depends on whether x is less than or greater than 2/3. The exact solution will be different in each case:

Case 1 (x < 2/3): x < -2 / (-3x + 2) Case 2 (x > 2/3): x > -2 / (-3x + 2)

These are the solutions to the given inequality based on the two different cases.