# How do you solve 9=7z-13z-21?

Apr 15, 2018

$z = - 5$

#### Explanation:

You combine $7 z$ and $- 13 z$ to get $- 6 z$, so

$9 = - 6 z - 21$

Add $21$ to both sides

$30 = - 6 z$

Divide both sides by $- 6$

$- 5 = z$

Apr 15, 2018

$z = - 5$

#### Explanation:

When solving equations, we can combine like terms as shown below:

$5 x + 4 x \to 9 x$

So to solve this problem, we need to isolate the variable "$z$"
We do this by combining all terms with the variable $z$ on them.

$9 = 7 z - 13 z - 21$

$9 = - 6 z - 21$

Then we treat it as a regular algebra problem by isolating the variable

$9 = - 6 z - 21$

$30 = - 6 z$

$z = - 5$

Note: Combining like terms can only be done with variables of the same degree, or in other words, variables raised to the same exponent. Example below:

$5 z + 3 {z}^{2}$ cannot be combined into one expression, but

$3 {z}^{2} + 5 {z}^{2}$ can be combined to produce $8 {z}^{2}$