Question

You are given that Z>2.

Write an inequality for each expression
a) 2z+9
b) 3(z-4)
c) 4+2z
d) 5(3z-2)

Answer 1

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)

--------------------------------------------------------------

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)

--------------------------------------------------------------

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)

--------------------------------------------------------------

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)

--------------------------------------------------------------

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.