Part (a)
Multiply both sides by 2, then add 9 to both sides.
z > 2
2z > 2*2
2z > 4
2z+9 > 4+9
2z+9 > 13 is the final answer for part (a)
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Part (b)
We'll start with subtracting 4 from both sides, and then triple each side.
z > 2
z-4 > 2-4
z-4 > -2
3(z-4) > 3*(-2)
3(z-4) > -6 is the final answer for part (b)
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Part (c)
Follow similar steps to that of part (a).
z > 2
2z > 2*2
2z > 4
2z+4 > 4+4
2z+4 > 8 is the final answer to part (c)
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Part (d)
For now let's ignore the 5 out front and focus on 3z-2
z > 2
3z > 3*2
3z > 6
3z-2 > 6-2
3z-2 > 4
Now multiply each side by 5.
5(3z-2) > 5*4
5(3z-2) > 20 is the final answer to part (d)
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Side note: The inequality signs did not flip when multiplying both sides by a positive number. The flip would only happen if we multiplied both sides by a negative number.