Questions: Consider the following inequality problem. 2z + 4 / 2 > 6 and -2(z - 2) > 16 Step 2 of 3: Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.

Consider the following inequality problem.
2z + 4 / 2 > 6 and -2(z - 2) > 16

Step 2 of 3: Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.

Transcript text: Consider the following inequality problem. \[ \frac{2 z+4}{2}>6 \quad \text { and } \quad-2(z-2)>16 \] Step 2 of 3 : Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.

Solution

Solution Steps

Step 1: Solve the second inequality

The second inequality is: $-2(z-2) > 16$

Step 2: Distribute the

-2

on the left side

$-2z + 4 > 16$

Step 3: Subtract 4 from both sides

$-2z > 12$

Step 4: Divide both sides by

-2

(remember to reverse the inequality sign when dividing by a negative number)

$z < -6$

Step 5: Express the solution in interval notation

The solution in interval notation is: $(-\infty, -6)$

Final Answer

$\boxed{(-\infty, -6)}$

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