Question

995. решите неравенства 1)|2х+1|<3 2)|2х+3|<4 3)|х+1|<2,5 4)|2х-5|<3 5)|2+3х|<7 6)2-5х|<8 ПОЖАЛУЙСТА УМОЛЯЮ, ПОМОГИТЕ, зарание спасибо!!!!!​

Answer 1

Ответ:

можно пожалуйста лучший ответ

Answer 2

Solution to the Inequalities:

To solve the given inequalities, let's solve each one separately:

1) |2x + 1| < 3: To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x + 1 > 0: In this case, the inequality becomes 2x + 1 < 3. Solving for x, we have: 2x + 1 < 3 2x < 3 - 1 2x < 2 x < 1

Case 2: 2x + 1 < 0: In this case, the inequality becomes -(2x + 1) < 3. Solving for x, we have: -(2x + 1) < 3 -2x - 1 < 3 -2x < 3 + 1 -2x < 4 x > -2

Therefore, the solution to the inequality |2x + 1| < 3 is -2 < x < 1.

2) |2x + 3| < 4: Again, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x + 3 > 0: In this case, the inequality becomes 2x + 3 < 4. Solving for x, we have: 2x + 3 < 4 2x < 4 - 3 2x < 1 x < 1/2

Case 2: 2x + 3 < 0: In this case, the inequality becomes -(2x + 3) < 4. Solving for x, we have: -(2x + 3) < 4 -2x - 3 < 4 -2x < 4 + 3 -2x < 7 x > -7/2

Therefore, the solution to the inequality |2x + 3| < 4 is -7/2 < x < 1/2.

3) |x + 1| < 2.5: Again, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: x + 1 > 0: In this case, the inequality becomes x + 1 < 2.5. Solving for x, we have: x + 1 < 2.5 x < 2.5 - 1 x < 1.5

Case 2: x + 1 < 0: In this case, the inequality becomes -(x + 1) < 2.5. Solving for x, we have: -(x + 1) < 2.5 -x - 1 < 2.5 -x < 2.5 + 1 -x < 3.5 x > -3.5

Therefore, the solution to the inequality |x + 1| < 2.5 is -3.5 < x < 1.5.

4) |2x - 5| < 3: Again, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x - 5 > 0: In this case, the inequality becomes 2x - 5 < 3. Solving for x, we have: 2x - 5 < 3 2x < 3 + 5 2x < 8 x < 4

Case 2: 2x - 5 < 0: In this case, the inequality becomes -(2x - 5) < 3. Solving for x, we have: -(2x - 5) < 3 -2x + 5 < 3 -2x < 3 - 5 -2x < -2 x > 1

Therefore, the solution to the inequality |2x - 5| < 3 is 1 < x < 4.

5) |2 + 3x| < 7: Again, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2 + 3x > 0: In this case, the inequality becomes 2 + 3x < 7. Solving for x, we have: 2 + 3x < 7 3x < 7 - 2 3x < 5 x < 5/3

Case 2: 2 + 3x < 0: In this case, the inequality becomes -(2 + 3x) < 7. Solving for x, we have: -(2 + 3x) < 7 -2 - 3x < 7 -3x < 7 + 2 -3x < 9 x > -3

Therefore, the solution to the inequality |2 + 3x| < 7 is -3 < x < 5/3.

6) 2 - 5x < 8: To solve this inequality, we need to isolate x. Subtracting 2 from both sides, we have: 2 - 5x < 8 -5x < 8 - 2 -5x < 6 Dividing both sides by -5 (and reversing the inequality sign), we have: x > 6/-5 x > -6/5

Therefore, the solution to the inequality 2 - 5x < 8 is x > -6/5.

In summary, the solutions to the given inequalities are: 1) -2 < x < 1 2) -7/2 < x < 1/2 3) -3.5 < x < 1.5 4) 1 < x < 4 5) -3 < x < 5/3 6) x > -6/5