Question

Рощвяжіть систему нерівностей Дають сто балів 2 - 5x < 7 ,\\ 3x+1<-8

Answer 1

Solving the System of Inequalities

To solve the system of inequalities, we will solve each inequality separately and then find the values of x that satisfy both inequalities.

The given system of inequalities is:

1. 2 - 5x < 7 2. 3x + 1 < -8

Let's solve each inequality step by step.

Solving the First Inequality

The first inequality is 2 - 5x < 7. To solve it, we will isolate x on one side of the inequality.

1. Subtract 2 from both sides of the inequality: 2 - 2 - 5x < 7 - 2 -5x < 5

2. Divide both sides of the inequality by -5. Since we are dividing by a negative number, the inequality sign will flip: (-5x) / -5 > 5 / -5 x > -1

So, the solution to the first inequality is x > -1.

Solving the Second Inequality

The second inequality is 3x + 1 < -8. Again, we will isolate x on one side of the inequality.

1. Subtract 1 from both sides of the inequality: 3x + 1 - 1 < -8 - 1 3x < -9

2. Divide both sides of the inequality by 3: (3x) / 3 < (-9) / 3 x < -3

So, the solution to the second inequality is x < -3.

Finding the Intersection of Solutions

To find the values of x that satisfy both inequalities, we need to find the intersection of the solution sets.

From the first inequality, we have x > -1, and from the second inequality, we have x < -3.

The values of x that satisfy both inequalities are the values that are greater than -1 and less than -3. However, there is no overlap between these two solution sets. Therefore, there are no values of x that satisfy both inequalities simultaneously.

In conclusion, the given system of inequalities does not have a solution.

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