Item 3

Find the sum.

-1/2 (7z+4) + 1/5 (5z-15)

We are given : - 1/2 (7z+4) + 1/5 (5z-15)

Solution: We have - 1/2 in front of parenthesis (7z+4) and 1/5 in front of parenthesis (5z-15).

That represents multiplication of - 1/2 by (7z+4) and multiplication of 1/5 by (5z-15).

So, we need to distribute - 1/2 over (7z+4) and 1/5 over (5z-15).

Therefore, - 1/2 (7z+4) + 1/5 (5z-15) = - 1/2 * 7z - 1/2 * 4 + 1/5*5z + 1/5 * - 15.

On simplifying this step, we get

-7/2 z - 2 + z - 3.

Now, we need to combine like terms.

We have like term of - 7/2 z is z and like term of - 2 is - 3.

Let us add those like terms.

-7/2 z + z: z could be written as z/1 to add with fraction - 7/2 z.

Therefore, - 7/2 z + z/1 = - 7/2 z + 2z/2 (we took common denomiator here)

= (-7+2) z/2

= - 5/2 z.

-2 - 3 = - 5.

Therefore,

-7/2 z - 2 + z - 3 = - 7/2 z + z - 2-3

= - 5/2 z - 5.

So, the final answer is - 5/2 z - 5.