Question

Решите неравенство :

Answer 1

Решение
cos2x ≥ - √2/2
- arccos(-√2/2) + 2πn ≤ 2x ≤ arccos(√2/2) + 2πn, n ∈ Z
3π/4 + 2πn ≤ 2x ≤ π/4 + 2πn, n ∈ Z
3π/8 + πn ≤ x ≤ π/8 + πn, n ∈ Z

Answer 2

Solving the Inequality

To solve the given inequality, we need to determine the values of x that satisfy the inequality. Let's break down the given inequality and solve it step by step.

The given inequality is not explicitly mentioned, so let's consider the different inequalities mentioned in the search results and solve them one by one.

1. \[4 - 3 - 5^2 - - 6\]

This expression does not represent an inequality. It seems to be an arithmetic expression that needs to be evaluated. Please provide the correct inequality so that we can solve it for you.

2. \[5x > 35\]

To solve this inequality, we need to isolate x on one side of the inequality sign. Let's divide both sides of the inequality by 5:

\[x > \frac{35}{5}\]

Simplifying further:

\[x > 7\]

Therefore, the solution to the inequality is x > 7.

3. \[log2(x-1) > 1\]

To solve this logarithmic inequality, we need to rewrite it in exponential form. The base of the logarithm is 2, and the exponent is 1. Therefore, we have:

\[2^1 > x - 1\]

Simplifying further:

\[2 > x - 1\]

Adding 1 to both sides of the inequality:

\[3 > x\]

Therefore, the solution to the inequality is x < 3.

4. \[3-2x > 7\]

To solve this inequality, we need to isolate x on one side of the inequality sign. Let's subtract 3 from both sides of the inequality:

\[-2x > 7 - 3\]

Simplifying further:

\[-2x > 4\]

Dividing both sides of the inequality by -2 (note that we need to reverse the inequality sign when dividing by a negative number):

\[x < \frac{4}{-2}\]

Simplifying further:

\[x < -2\]

Therefore, the solution to the inequality is x < -2.

5. \[(14-7x)(x+3) > 0\]

To solve this inequality, we can use the concept of intervals and test the sign of the expression for different intervals of x.

- Interval 1: x < -3 - Choose x = -4: \[(14-7(-4))( (-4)+3) = (14+28)(-1) = -42 < 0\] - The expression is negative in this interval.

- Interval 2: -3 < x < 2 - Choose x = 0: \[(14-7(0))( (0)+3) = (14)(3) = 42 > 0\] - The expression is positive in this interval.

- Interval 3: x > 2 - Choose x = 3: \[(14-7(3))( (3)+3) = (14-21)(6) = -42 < 0\] - The expression is negative in this interval.

Therefore, the solution to the inequality is x < -3 or 2 < x.

Please provide the correct inequality if none of the above options match the one you intended to solve.