Question

Решите систему неравенств 3-2x / 5>1 x^2-4> или равно 0

Answer 1

Решение во вложении.

Answer 2

Solving the System of Inequalities

To solve the system of inequalities 3-2x/5 > 1 and x^2-4 ≥ 0, we can follow these steps:

1. Solve the first inequality 3-2x/5 > 1 to find the range of values for x. 2. Solve the second inequality x^2-4 ≥ 0 to find the range of values for x. 3. Find the intersection of the ranges obtained from the two inequalities to determine the solution set for the system of inequalities.

Let's solve each inequality step by step.

Solving the First Inequality

The first inequality is 3-2x/5 > 1. We can solve it as follows:

3-2x/5 > 1

-2x/5 > 1 - 3

-2x/5 > -2

To solve for x, we multiply both sides by -5 (note that multiplying or dividing by a negative number reverses the inequality sign):

-2x > -2 * (-5)

-2x > 10

Now, divide both sides by -2. When dividing by a negative number, remember to reverse the inequality sign:

x < 10 / -2

x < -5

So, the solution to the first inequality is x < -5.

Solving the Second Inequality

The second inequality is x^2-4 ≥ 0. We can solve it as follows:

x^2-4 ≥ 0

This is a quadratic inequality. We can solve it by finding the critical points and testing the intervals.

The critical points are where the expression equals zero:

x^2-4 = 0

x^2 = 4

x = ±2

Now, we test the intervals created by the critical points:

- For x < -2, we have (x+2)(x-2) > 0 - For -2 ≤ x ≤ 2, we have (x+2)(x-2) ≥ 0 - For x > 2, we have (x+2)(x-2) > 0

So, the solution to the second inequality is -2 ≤ x ≤ 2.

Finding the Intersection

To find the intersection of the ranges obtained from the two inequalities, we look for the overlapping values. The solution set for the system of inequalities is the intersection of the individual solution sets.

The overlapping values are between -5 and 2.

Therefore, the solution to the system of inequalities 3-2x/5 > 1 and x^2-4 ≥ 0 is:

-5 < x ≤ 2.

This is the range of values for x that satisfy both inequalities.

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