Question

Решите систему неравенств. 6.2х - 8< 4,4х + 2,8,8х -11 > 5х - 14.​

Answer 1

Ответ:

$6.2x - 4.4x < 2.8 + 8 \\ 1.8x < 10.8 \\ x < 10.8 \div 1.8 \\ x < 6$

$8x - 5x > - 14 + 11 \\ 3x > 14 + 11 \\ 3x > - 3 \\ x > - 3 \div 3 \\ x > - 1$

На держи ))

Answer 2

Solving the System of Inequalities

To solve the system of inequalities 6.2x - 8 < 4 and 4x + 2.8 > 8x - 11, we can follow these steps:

1. Solve the first inequality: 6.2x - 8 < 4 2. Solve the second inequality: 4x + 2.8 > 8x - 11 3. Find the values of x that satisfy both inequalities simultaneously.

Solving the First Inequality

To solve the inequality 6.2x - 8 < 4, we can add 8 to both sides of the inequality to isolate the term with x:

6.2x - 8 + 8 < 4 + 8 6.2x < 12

Now, divide both sides by 6.2 to solve for x:

x < 12 / 6.2 x < 1.935

So, the solution to the first inequality is x < 1.935.

Solving the Second Inequality

To solve the inequality 4x + 2.8 > 8x - 11, we can start by simplifying the inequality:

4x - 8x > -11 - 2.8 -4x > -13.8

Dividing both sides by -4 requires reversing the inequality sign:

x < -13.8 / -4 x < 3.45

So, the solution to the second inequality is x < 3.45.

Finding the Common Solution

To find the values of x that satisfy both inequalities simultaneously, we need to find the intersection of their solution sets. Since both inequalities have x less than a certain value, the common solution is the intersection of these intervals, which is x < 1.935 and x < 3.45.

Therefore, the solution to the system of inequalities 6.2x - 8 < 4 and 4x + 2.8 > 8x - 11 is x < 1.935.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.