Question

Укажіть найменше ціле число, що є розв’язком системи нерівностей {2x ≤ 3, {x − 7 > −2. Посмотреть ответы sonealya sonealya Решение на фото. Ответ: пустое множество. miskovbohdan07 miskovbohdan07 Объяснение: 2x≤3 x-7>-2 x≤3/2 x>-2+7 x≤3/2 x>5 xє(5;3/2]Система нерівностей не виконується

Answer 1

System of Inequalities

The given system of inequalities is:

1. 2x ≤ 3 2. x - 7 > -2

To find the least integer that satisfies this system of inequalities, let's solve it step by step.

Solving the First Inequality

The first inequality is 2x ≤ 3. To solve it, we need to isolate the variable x.

1. Divide both sides of the inequality by 2: x ≤ 3/2

So, the solution to the first inequality is x ≤ 3/2.

Solving the Second Inequality

The second inequality is x - 7 > -2. Again, we need to isolate the variable x.

1. Add 7 to both sides of the inequality: x > 5

So, the solution to the second inequality is x > 5.

Combining the Inequalities

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

1. The first inequality is x ≤ 3/2. 2. The second inequality is x > 5.

Since there is no overlap between the two inequalities, there is no value of x that satisfies both inequalities simultaneously. Therefore, the solution to the system of inequalities is an empty set.

In conclusion, the least integer that satisfies the given system of inequalities is an empty set.