Question

Решите систему неравенств срочно, пожалуйста! {7x≤42 -2x<4 Смотреть ответ alexproVip alexproVip Ответ:(2;6]Пошаговое объяснение:7x≤42/:7,. x≤6-2x<4/:(-2). x>2

Answer 1

Solving the System of Inequalities

To solve the system of inequalities 7x ≤ 42 and -2x < 4, we will follow these steps:

Step 1: Solve the first inequality, 7x ≤ 42. - Divide both sides of the inequality by 7 to isolate x: x ≤ 6. [[1]]

Step 2: Solve the second inequality, -2x < 4. - Divide both sides of the inequality by -2. Since we are dividing by a negative number, the direction of the inequality sign will change: x > -2. [[2]]

Step 3: Combine the solutions from Step 1 and Step 2. - The solution to the system of inequalities is the intersection of the individual solutions. In this case, the intersection is the values of x that satisfy both inequalities. - Since x ≤ 6 and x > -2, the overlapping region is x > -2 and x ≤ 6.

Therefore, the solution to the system of inequalities is (2, 6]. This means that x can take any value greater than -2 and less than or equal to 6.

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