`(z)/(6)((3)/(2))-7=-2(3z-4)`
Which value of z satisfies the equation above?

Options

A. `-(21)/(5)`
B. `(-4)/(25)`
C. `(4)/(25)`
D. `(12)/(5)`

Answer

D

Explanation

Difficult: Easy
Category: Heart of Algebra/ Linear Equations
Strategic Advice: Some questions, like this one are intended to test your fluency with algebraic manipulations, so work carefully and you'll arrive at the correct answer.
Getting to the Answer: Simplify the left side of the equation using multiplications and the right side using the distributive property. Be sure to distribute the negative sign to both terms inside the parentheses on the right side. Next, collect the variable terms on one side of the equation and constant on the other, and then solve for z using inverse operations:
`(z)/(6)((3)/(2))-7=-2(3z-4)`
`(z)/(4)-7=-6z+8`
`(z)/(4)=-6z+15`
`4*[(z)/(4)]+4*[-6z+15]`
`z=-24z+60`
`25z=60`
`z=(60)/(25)=(12)/(5)`
The correct answer is (D).