Question

ОЧЕНЬ СРОЧНО! ПОМОГИТЕ, ПОЖАЛУЙСТА! Найдите все значения параметра a, при которых неравенство /x+1/-/2x-2/≦a выполняется при всех значениях -2≦x≦7. Желательно с подробным объяснением

Answer 1

формулам ctg 2x = cos 2x / sin 2x, tg x = sinx/cos 

Answer 2

Finding the Values of Parameter a in the Inequality

To find the values of the parameter a for which the inequality |x + 1| - |2x - 2| ≤ a holds true for all values of -2 ≤ x ≤ 7, we can break down the problem into different intervals based on the absolute value expressions.

Let's consider three intervals: x ≤ -1, -1 < x ≤ 1, and x > 1.

Interval 1: x ≤ -1

In this interval, both x + 1 and 2x - 2 are negative. Therefore, the inequality becomes:

-(x + 1) - (-(2x - 2)) ≤ a

Simplifying this expression, we get:

-x - 1 + 2x - 2 ≤ a

Combining like terms, we have:

x - 3 ≤ a

Interval 2: -1 < x ≤ 1

In this interval, x + 1 is positive, but 2x - 2 is negative. Therefore, the inequality becomes:

(x + 1) - (-(2x - 2)) ≤ a

Simplifying this expression, we get:

x + 1 + 2x - 2 ≤ a

Combining like terms, we have:

3x - 1 ≤ a

Interval 3: x > 1

In this interval, both x + 1 and 2x - 2 are positive. Therefore, the inequality becomes:

(x + 1) - (2x - 2) ≤ a

Simplifying this expression, we get:

x + 1 - 2x + 2 ≤ a

Combining like terms, we have:

-x + 3 ≤ a

Combining the Intervals

To find the values of a that satisfy the inequality for all values of -2 ≤ x ≤ 7, we need to consider the intersection of the intervals.

For x ≤ -1, the inequality is x - 3 ≤ a.

For -1 < x ≤ 1, the inequality is 3x - 1 ≤ a.

For x > 1, the inequality is -x + 3 ≤ a.

To satisfy the inequality for all values of -2 ≤ x ≤ 7, we need to find the maximum lower bound and the minimum upper bound for a among these intervals.

The maximum lower bound for a is the largest value that satisfies all the lower bounds from each interval. In this case, it is a = max(x - 3, 3x - 1, -x + 3).

The minimum upper bound for a is the smallest value that satisfies all the upper bounds from each interval. In this case, it is a = min(x - 3, 3x - 1, -x + 3).

By finding the maximum lower bound and the minimum upper bound for a, we can determine the range of values for a that satisfy the inequality for all values of -2 ≤ x ≤ 7.

Please note that the specific values of a will depend on the values of x within the given range.