Question

Solve for x: 2/3(x − 2) = 4x.

A. x = -2/5
B. x = -5/2
C. x = 2/5
D. x = −2

Answer 1

a

Explanation:

Answer 2

`\large\boxed{A.\ x=-(2)/(5)}`

Explanation:

`(2)/(3)(x-2)=4x\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot(2)/(3\!\!\!\!\diagup_1)(x-2)=(3)(4x)\\\\2(x-2)=12x\qquad\text{divide both sides by 2}\\\\(2\!\!\!\!\diagup^1(x-2))/(2\!\!\!\!\diagup_1)=(12\!\!\!\!\!\diagup^6x)/(2\!\!\!\!\diagup_1)\\\\x-2=6x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x-x-2=6x-x\\\\-2=5x\qquad\text{divide both sides by 5}\\\\(-2)/(5)=(5\!\!\!\!\diagup^1x)/(5\!\!\!\!\diagup_1)\\\\-(2)/(5)=x\to x=-(2)/(5)`