Question

X(4-x) ——-< или =0 5x+10

Answer 1

Ответ:

решение предоставлено на фото

Answer 2

To solve the inequality, let's break it down into two separate cases:

Case 1: X(4 - x) = 0 In this case, either X = 0 or (4 - x) = 0.

If X = 0, then the inequality becomes: 5x + 10 ≤ 0 5(0) + 10 ≤ 0 10 ≤ 0

However, 10 is not less than or equal to 0, so X = 0 does not satisfy the inequality.

If (4 - x) = 0, then x = 4. Substituting this value back into the inequality: 5x + 10 ≤ 0 5(4) + 10 ≤ 0 20 + 10 ≤ 0 30 ≤ 0

Again, 30 is not less than or equal to 0, so x = 4 does not satisfy the inequality.

Case 2: X(4 - x) < 0 In this case, X and (4 - x) have opposite signs.

If X > 0, then (4 - x) < 0. 4 - x < 0 4 < x

Now let's consider the condition 5x + 10 ≤ 0: 5x + 10 ≤ 0 5x ≤ -10 x ≤ -2

Combining the two conditions, we have 4 < x ≤ -2.

If X < 0, then (4 - x) > 0. 4 - x > 0 4 > x

Again, considering the condition 5x + 10 ≤ 0: 5x + 10 ≤ 0 5x ≤ -10 x ≤ -2

Combining the two conditions, we have x < 4 and x ≤ -2.

Therefore, the solution to the inequality X(4 - x) ≤ 5x + 10 is: 4 < x ≤ -2 or x < 4 and x ≤ -2.