Question

4. Розв'язати нерівності : 1) 2x - 9 < x + 5 2) 4(x - 3) + 1 > 12 - 3(1 - 2x) 3) 3(x + 1) > x + 5 4) (8x + 1)/3 <= (7x - 5)/4

Answer 1

Ответ:

попробуй програму Photometh

Answer 2

1) 2x - 9 < x + 5 First, let's subtract x from both sides: 2x - x - 9 < 5 Then, combine like terms: x - 9 < 5 Now, add 9 to both sides: x < 14

2) 4(x - 3) + 1 > 12 - 3(1 - 2x) First, let's distribute the 4 on the left side and the -3 on the right side: 4x - 12 + 1 > 12 - 3 + 6x Combine like terms: 4x - 11 > 9 + 6x Subtract 6x from both sides: -2x - 11 > 9 Add 11 to both sides: -2x > 20 Now, divide by -2 (remembering to reverse the inequality when dividing by a negative number): x < -10

3) 3(x + 1) > x + 5 First, distribute the 3 on the left side: 3x + 3 > x + 5 Subtract x from both sides: 2x + 3 > 5 Subtract 3 from both sides: 2x > 2 Divide by 2: x > 1

4) (8x + 1)/3 <= (7x - 5)/4 First, let's clear the fractions by multiplying through by the least common multiple of 3 and 4, which is 12: 4(8x + 1) <= 3(7x - 5) Expand and simplify: 32x + 4 <= 21x - 15 Subtract 21x from both sides: 11x + 4 <= -15 Subtract 4 from both sides: 11x <= -19 Divide by 11: x <= -19/11

So, the solutions to the inequalities are: 1) x < 14 2) x < -10 3) x > 1 4) x <= -19/11