# How do you solve the equation for z: 4(2z - 3) = 7(z + 5)?

Jul 7, 2015

There are several steps.

#### Explanation:

I will remove parentheses, then collect all terms involving the unknown on one side and all terms not involving the unknown on the other side. I then expect to divide by the coefficient of the unknown.

$4 \left(2 z - 3\right) = 7 \left(z + 5\right)$

Remove parentheses by using the distributive property (of multiplication over addition and subtraction).

$4 \left(2 z\right) - 4 \left(3\right) = 7 \left(z\right) + 7 \left(5\right)$

$8 z - 12 = 7 z + 35$

Subtract $7 z$ and add $12$ on both sides:

$8 z - 7 z = 35 + 12$

$z = 47$

In this case, the coefficient of the unknown (the number in front of $z$) is $1$ (not written), so I do not need to divide. We can see that the solution is:

$47$

The solution set is: $\left\{47\right\}$.