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

1 Answer
Jul 7, 2015

Answer:

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(2z - 3) = 7(z + 5)#

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

#4(2z) - 4(3) = 7(z) +7(5)#

#8z-12 = 7z +35#

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

#8z - 7z = 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: #{47}#.