Solve the system 2x ≥ 4 and 2x ≤ 6. The solution for x is

Solve the system 2x ≥ 4 and 2x ≤ 6. The solution for x is

• A. x ∈ [2,3]
• B. x ∈ [2,4]
• C. x ∈ [0,3]
• D. x ∈ (-∞, ∞)

Answer: (A)

Solving a system of inequalities by taking the overlap of their solution sets. For each inequality, solve to find the range of x that satisfies it, then intersect those ranges. From 2x ≥ 4, divide by 2 to get x ≥ 2. From 2x ≤ 6, divide by 2 to get x ≤ 3. Both conditions must hold, so x must be at least 2 and at most 3. The numbers that satisfy both are exactly x ∈ [2,3]. That’s why the solution is x in [2,3]. The other options don’t fit because they either include values less than 2 or greater than 3, which violate one of the two inequalities, or they ignore the constraints entirely.

Solving a system of inequalities by taking the overlap of their solution sets. For each inequality, solve to find the range of x that satisfies it, then intersect those ranges.

From 2x ≥ 4, divide by 2 to get x ≥ 2. From 2x ≤ 6, divide by 2 to get x ≤ 3. Both conditions must hold, so x must be at least 2 and at most 3. The numbers that satisfy both are exactly x ∈ [2,3].

That’s why the solution is x in [2,3]. The other options don’t fit because they either include values less than 2 or greater than 3, which violate one of the two inequalities, or they ignore the constraints entirely.