Question

1) До розв'язків якої з наведених нерівностей належить число 1 &x-5>1; B) /x - 20; Г) 2x −5>-4. 3 A) x² -1>0; Б) 2) Укажіть найбільший цілий розв'язок нерівності x ≤ −9,8. A) -9; Б) -10; В) 0; Г) –9,8. 3) Знайдіть суму натуральних розв’язків нерівності x ≤ 3,5. а) 3; 6) 6; в) 4; г) 5. 4

Answer 1

1) До розв'язків нерівностей належить число: a) 1 + x > 5 b) 1 / x - 20 c) 2x - 5 > -4 d) x² - 1 > 0

To solve these inequalities, let's go through each one separately:

a) 1 + x > 5 Subtracting 1 from both sides, we get: x > 4 Therefore, any number greater than 4 is a solution to this inequality.

b) 1 / x - 20 Adding 20 to both sides, we get: 1 / x > 20 Multiplying both sides by x (remembering that x cannot be 0), we get: 1 > 20x Dividing both sides by 20, we get: 1/20 > x This means that any number less than 1/20 is a solution to this inequality.

c) 2x - 5 > -4 Adding 5 to both sides, we get: 2x > 1 Dividing both sides by 2, we get: x > 1/2 Therefore, any number greater than 1/2 is a solution to this inequality.

d) x² - 1 > 0 Factoring the left side, we get: (x - 1)(x + 1) > 0 This inequality is true when either both factors are positive or both factors are negative. When x < -1, both factors are negative and the inequality holds. When -1 < x < 1, the first factor is negative and the second factor is positive, so the inequality does not hold. When x > 1, both factors are positive and the inequality holds. Therefore, the solutions to this inequality are x < -1 or x > 1.

2) Укажіть найбільший цілий розв'язок нерівності x ≤ -9,8. The largest integer solution to x ≤ -9.8 is -10.

3) Знайдіть суму натуральних розв’язків нерівності x ≤ 3.5. The natural number solutions to x ≤ 3.5 are 1, 2, and 3. The sum of these numbers is 1 + 2 + 3 = 6.

Therefore, the answers are: 1) a) x > 4 b) x < 1/20 c) x > 1/2 d) x < -1 or x > 1

2) Б) -10

3) г) 6