Question

Help me, which one is it? The system of inequality is y ≥ 4 and y > |2x + 4|.

a) y ≤ 4
b) y ≥ -4
c) y ≥ 2x + 4
d) y ≤ -2x - 4

Answer 1

The correct system of inequality is y ≤ -2x - 4.

Step-by-step explanation:

The system of inequality is y ≥ 4 and y > |2x + 4|.

To find the correct inequality, we need to consider two cases:

1. Case 1: If 2x + 4 ≥ 0
2. In this case, the inequality becomes y > 2x + 4, which means that y is greater than the expression 2x + 4.
3. Case 2: If 2x + 4 < 0
4. In this case, the inequality becomes y > -(2x + 4), which means that y is greater than the negative of the expression 2x + 4.

Combining these two cases, we can write the inequality as y > max(2x + 4, -(2x + 4)), since the absolute value function outputs the greater value.

Simplifying this, we get y > max(2x + 4, -2x - 4), which can be further simplified to y > -2x - 4.

Therefore, the correct answer is d) y ≤ -2x - 4.