Question

Решить неравенство x(3x-1)-x^2+16≤x(2-x)-x(11-2x)

Answer 1

Ответ:да че там решать просто скобки раскрой и х в одну часть перенеси

Объяснение:

Answer 2

To solve the inequality, let's first simplify both sides of the inequality and then find the solution for 'x'. The given inequality is:

x(3x-1) - x^2 + 16 ≤ x(2-x) - x(11-2x)

Step 1: Simplify both sides of the inequality

x(3x - 1) - x^2 + 16 ≤ x(2 - x) - x(11 - 2x)

Expand the expressions:

3x^2 - x - x^2 + 16 ≤ 2x - x^2 - 11x + 2x^2

Combine like terms:

2x^2 - x + 16 ≤ x^2 - 9x

Step 2: Move all terms to one side of the inequality (in this case, to the left side):

2x^2 - x + 16 - x^2 + 9x ≤ 0

Step 3: Combine like terms:

x^2 + 8x + 16 ≤ 0

Step 4: Factorize the quadratic expression:

(x + 4)(x + 4) ≤ 0

Step 5: Find the critical points (where the expression equals zero):

x + 4 = 0

x = -4

Step 6: Create a sign chart to determine the solution:

We need to check the signs of the expression (x + 4)(x + 4) in three intervals:

1. x < -4
2. x = -4
3. x > -4

Now, let's test a value in each interval to determine the sign:

1. Pick x = -5 (x < -4):

(-5 + 4)(-5 + 4) = (-1)(-1) = 1 (Positive)

2. Pick x = -4 (x = -4):

(-4 + 4)(-4 + 4) = (0)(0) = 0 (Zero)

3. Pick x = -3 (x > -4):

(-3 + 4)(-3 + 4) = (1)(1) = 1 (Positive)

Step 7: Determine the solution:

The inequality is satisfied for x values where the expression (x + 4)(x + 4) is less than or equal to zero.

Looking at the sign chart, the solution is:

x ∈ [-4]

So, the solution to the inequality is x ≤ -4.