Question

2x+7>0 25+6x>1 Решите систему неравенств

Answer 1

2x>-7
6x>1-25

x>-3.5
x>-4

Answer 2

To solve the system of inequalities 2x + 7 > 0 and 25 + 6x > 1, we will solve each inequality separately and then find the intersection of their solution sets.

Solving the inequality 2x + 7 > 0:

To solve this inequality, we need to isolate x on one side of the inequality sign. Here's how we can do it:

2x + 7 > 0 Subtract 7 from both sides: 2x > -7 Divide both sides by 2 (since the coefficient of x is 2 and we want to isolate x): x > -7/2

So the solution to the inequality 2x + 7 > 0 is x > -7/2.

Solving the inequality 25 + 6x > 1:

Similarly, we will isolate x on one side of the inequality sign:

25 + 6x > 1 Subtract 25 from both sides: 6x > -24 Divide both sides by 6: x > -4

So the solution to the inequality 25 + 6x > 1 is x > -4.

Finding the intersection of the solution sets:

To find the intersection of the solution sets, we need to find the values of x that satisfy both inequalities. In this case, we need to find the values of x that are greater than -7/2 and greater than -4.

Since both inequalities have the same direction (greater than), the intersection of their solution sets is the solution set of the inequality with the stricter condition. In this case, x > -4 is the stricter condition.

Therefore, the solution to the system of inequalities 2x + 7 > 0 and 25 + 6x > 1 is x > -4.

I hope this helps! Let me know if you have any further questions.