Which of the following represents the solution of 3/2 = 3x/2x minus 6/5X a) x=1/5 b)x=5/9 c)all real numbers d)no solution (im pretty bad at math)

Question

asked Sep 20, 2020 55.8k views

2 Answers

Iceqing · Answer 1 · 2020-09-26T06:23:29+0000

Answer: d) No solution.

Explanation:

Given the equation:

(3)/(2)=(3x)/(2x)-(6)/(5x)

The denominator of the fractions cannot be zero, then, the Domain is:

$x\\eq 0$

Simplify:

(3)/(2)=(3)/(2)-(6)/(5x)

Subtract
(3)/(2) from both sides of the equation. Then you get:

$(3)/(2)-((3)/(2))=(3)/(2)-(6)/(5x)-((3)/(2))\\\\0=-(6)/(5x)$

Multiply both sides of the equation by
(
$5x \\eq 0$ ), then:

(5x)(0)=(-(6)/(5x))(5x)

Since the multiplication of
by zero is zero, you get:

0=-6 (This is FALSE)

Therefore, since there is no value for the variable that makes the equation true, the equation has NO SOLUTION.