Question

Розв'яжіть нерівність -9 < 2х - 5 < 9. З варіантів відповідей оберіть: - довжину проміжку, що є розв'язком нерівності; - кількість цілих розв'язків нерівності; - суму цілих розв'язків нерівності Срочно Дам 30 баллов ПЖ!!!!!!

Answer 1

Ответ:

X Є (-2 , 7) ...

................

Answer 2

Solving the Inequality

To solve the inequality -9 < 2x - 5 < 9, we need to find the range of values for x that satisfy the inequality. Let's break it down into two separate inequalities:

1. -9 < 2x - 5 2. 2x - 5 < 9

Let's solve each inequality separately:

1. -9 < 2x - 5: - Add 5 to both sides: -9 + 5 < 2x - 5 + 5 - Simplify: -4 < 2x - Divide both sides by 2 (since the coefficient of x is 2): -4/2 < 2x/2 - Simplify: -2 < x

2. 2x - 5 < 9: - Add 5 to both sides: 2x - 5 + 5 < 9 + 5 - Simplify: 2x < 14 - Divide both sides by 2: 2x/2 < 14/2 - Simplify: x < 7

Range of Values for x

From the above inequalities, we have found that -2 < x < 7. This means that the range of values for x that satisfy the inequality -9 < 2x - 5 < 9 is -2 < x < 7.

Number of Integer Solutions

To determine the number of integer solutions, we need to find the integers within the range -2 < x < 7. The integers that satisfy this condition are -1, 0, 1, 2, 3, 4, 5, 6. Therefore, there are 8 integer solutions.

Sum of Integer Solutions

To find the sum of the integer solutions, we add up all the integers within the range -2 < x < 7. The sum of the integer solutions is -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 = 20.

Therefore, the options for the given inequality are: - Length of the interval that is a solution to the inequality: -2 < x < 7 - Number of integer solutions to the inequality: 8 - Sum of the integer solutions to the inequality: 20.