Question

Solve the system of inequalities 0.8x-3<=0,4.1x>=8.2

Answer 1

To solve the system of inequalities 0.8x-3 ≤ 0 and 4.1x ≥ 8.2, divide and isolate x in each inequality resulting in x ≤ 3.75 and x ≥ 2.

Step-by-step explanation:

To solve the system of inequalities 0.8x-3 ≤ 0 and 4.1x ≥ 8.2, we need to find the values of x that satisfy both inequalities.

For the first inequality, 0.8x-3 ≤ 0, we add 3 to both sides to isolate x and get 0.8x ≤ 3. Then, we divide both sides by 0.8 to get x ≤ 3/0.8 = 3.75.

For the second inequality, 4.1x ≥ 8.2, we divide both sides by 4.1 to isolate x and get x ≥ 8.2/4.1 = 2. Therefore, the values of x that satisfy both inequalities are x ≤ 3.75 and x ≥ 2.

Answer 2

Therefore, the values of x that satisfy both inequalities are those that are greater than or equal to 2 and less than or equal to 3.75.

Here's the solution to the system of inequalities 0.8x - 3 <= 0, 4.1x >= 8.2:

1. Solve the first inequality, 0.8x - 3 <= 0:

Add 3 to both sides: 0.8x <= 3

Divide both sides by 0.8: x <= 3.75

2. Solve the second inequality, 4.1x >= 8.2:

Divide both sides by 4.1: x >= 2

3. Combine the solutions:

The solution to the system of inequalities is the intersection of the individual solutions, which is **2 <= x <= 3.75