Question

1) x^2-x>6 2)x^2+11x>или равно-30

Answer 1

Ответ:

1) (- безкінечність; - 2)U(3;+ безкі..)

2)(- безкі...;-5]

Answer 2

1. To solve the inequality $x^2 - x > 6$, follow these steps:

Step 1: Move all terms to one side of the inequality: $x^2 - x - 6 > 0$

Step 2: Factor the quadratic expression: $(x - 3)(x + 2) > 0$

Step 3: Determine the sign of the expression in each interval:

Interval 1: $x < -2$ Both factors are negative, so the expression is positive: $( - ) \cdot ( - ) = +$

Interval 2: $-2 < x < 3$ The first factor is negative and the second factor is positive, so the expression is negative: $( - ) \cdot ( + ) = -$

Interval 3: $x > 3$ Both factors are positive, so the expression is positive: $( + ) \cdot ( + ) = +$

Step 4: Combine the intervals where the expression is positive: $x < -2 \text{ or } x > 3$

Therefore, the solution to the inequality $x^2 - x > 6$ is $x < -2$ or $x > 3$.

2. To solve the inequality $x^2 + 11x \geq -30$, follow these steps:

Step 1: Move all terms to one side of the inequality: $x^2 + 11x + 30 \geq 0$

Step 2: Factor the quadratic expression: $(x + 5)(x + 6) \geq 0$

Step 3: Determine the sign of the expression in each interval:

Interval 1: $x < -6$ Both factors are negative, so the expression is positive: $( - ) \cdot ( - ) = +$

Interval 2: $-6 < x < -5$ The first factor is negative and the second factor is positive, so the expression is negative: $( - ) \cdot ( + ) = -$

Interval 3: $x > -5$ Both factors are positive, so the expression is positive: $( + ) \cdot ( + ) = +$

Step 4: Combine the intervals where the expression is positive: $x < -6 \text{ or } x > -5$

Therefore, the solution to the inequality $x^2 + 11x \geq -30$ is $x < -6$ or $x > -5$.