Question

25 POINTS!!! Which number could be multiplied by each side of the equation to produce the equivalent equation x=15?

2/3x=10

A. 3

B.3/2

C.-2/3

D. 1/3

Answer 1

`\large\boxed{B.\ (3)/(2)}`

Explanation:

`(2)/(3)x=10\qquad\text{divide both sides by}\ (2)/(3)\\\\\text{Divide by a fraction is the same as multiply by the  reciprocal of this fraction.}\\\text{divide both sides by}\ (2)/(3)\ \text{is the same as multiply both sides by}\ (3)/(2)\\\\(3\!\!\!\!\diagup^1)/(2\!\!\!\!\diagup_1)\cdot(2\!\!\!\!\diagup^1)/(3\!\!\!\!\diagup_1)x=(3)/(2\!\!\!\!\diagup_1)\cdot10\!\!\!\!\!\diagup^5\\\\x=(3)(5)\\\\x=15`