Question

-5x(x+6)≥(x-3)-10алгебра 9 класс​

Answer 1

Решение на приложенной фотографии:

Answer 2

To solve the inequality -5x(x + 6) ≥ (x - 3) - 10, we'll start by simplifying both sides of the inequality and then solving for x. Let's go step by step:

Step 1: Expand and simplify both sides of the inequality: -5x(x + 6) ≥ (x - 3) - 10

Start with the left side: -5x(x + 6) = -5x^2 - 30x

Now simplify the right side: (x - 3) - 10 = x - 3 - 10 = x - 13

So the inequality becomes: -5x^2 - 30x ≥ x - 13

Step 2: Move all terms to one side of the inequality to get a quadratic inequality equal to zero: -5x^2 - 30x - x + 13 ≥ 0

Combine like terms: -5x^2 - 31x + 13 ≥ 0

Step 3: Solve the quadratic inequality. There are different methods to solve this type of inequality. One common method is to find the roots of the quadratic equation and use test intervals.

To find the roots, set the inequality equal to zero: -5x^2 - 31x + 13 = 0

This quadratic equation does not factor easily, so we can use the quadratic formula to find the roots: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -5, b = -31, and c = 13. Plugging in these values: x = (-(-31) ± √((-31)^2 - 4(-5)(13))) / (2(-5)) x = (31 ± √(961 + 260)) / (-10) x = (31 ± √1221) / (-10)

The roots of the equation are approximately x ≈ -0.263 and x ≈ 4.963.

Step 4: Use the test intervals to determine the solution set for the inequality.

Choose a test point within each interval: For x < -0.263, let's choose x = -1. For -0.263 < x < 4.963, let's choose x = 0. For x > 4.963, let's choose x = 5.

Evaluate the inequality for each test point: For x = -1: -5(-1)^2 - 31(-1) + 13 ≥ 0 -5 + 31 + 13 ≥ 0 39 ≥ 0 This is true.

For x = 0: -5(0)^2 - 31(0) + 13 ≥ 0 0 + 0 + 13 ≥ 0 13 ≥ 0 This is also true.

For x = 5: -5(5)^2 - 31(5) + 13 ≥ 0 -125 - 155 + 13 ≥ 0 -267 ≥ 0 This is false.

Step 5: Analyzing the results of the test intervals:

• For x < -0.263, the inequality holds true.
• For -0.263 < x < 4.963, the inequality holds true.
• For x > 4.963, the inequality does not hold true.

Step 6: Write the solution set: Since the inequality holds true for x < -0.263 and -0.263 < x < 4.963, the solution set is: x < -0.263 or -0.263 < x < 4.963.