Question

3+2x>5-x 1-2(x-1.5≤-5, 3x+4.5<27-1.5xответ:[ ; ]​

Answer 1

Ответ:

Пошаговое объяснение:

3+2х>5-х

3х>2

х>2/3

х∈(2/3 ; +∞)

1-2(х-1,5)≤ - 5

1-2х+3≤-5

2х≥4+5

х≥9/4 ;  (х≥2,25).

х∈[2,25; +∞).

3х+4,5<27-1,5х

4,5х<22,5

х<5

х∈(-∞; 5)

Для системы общий ответ:

х∈[2,25; 5)

Answer 2

To solve this system of inequalities, we'll address each inequality separately and then find the intersection of their solution sets. Let's start with the first inequality:

1. 3 + 2x > 5 - x

We can simplify this inequality:

3 + 2x > 5 - x Add x to both sides: 3 + 2x + x > 5 Combine like terms: 3 + 3x > 5 Subtract 3 from both sides: 3x > 5 - 3 3x > 2 Divide by 3 (note: since we're dividing by a positive number, we don't need to change the direction of the inequality): x > 2/3

So, the solution to the first inequality is x > 2/3.

Now, let's move on to the second inequality:

2. 1 - 2(x - 1.5) ≤ -5

We can simplify this inequality:

1 - 2(x - 1.5) ≤ -5 Distribute the -2 on the left side: 1 - 2x + 3 ≤ -5 Combine like terms: -2x + 4 ≤ -5 Subtract 4 from both sides: -2x ≤ -5 - 4 -2x ≤ -9 Divide by -2 (note: when dividing by a negative number, we need to reverse the direction of the inequality): x ≥ -9/(-2) x ≥ 9/2

So, the solution to the second inequality is x ≥ 9/2.

Finally, let's address the third inequality:

3. 3x + 4.5 < 27 - 1.5x

We can simplify this inequality:

3x + 4.5 < 27 - 1.5x Add 1.5x to both sides: 3x + 1.5x + 4.5 < 27 Combine like terms: 4.5x + 4.5 < 27 Subtract 4.5 from both sides: 4.5x < 27 - 4.5 4.5x < 22.5 Divide by 4.5 (note: since we're dividing by a positive number, we don't need to change the direction of the inequality): x < 22.5/4.5 x < 5

So, the solution to the third inequality is x < 5.

Now, let's find the intersection of these solutions:

x > 2/3 (from the first inequality) x ≥ 9/2 (from the second inequality) x < 5 (from the third inequality)

The intersection of these solution sets is the set of values that satisfy all three inequalities, so the final answer is:

$x \in \left(\frac{9}{2}, 5\right)$