What number should both sides of the equation x/-5=_6 be multiplied by to solve for the value of x?
To solve for the value of x in the equation x/-5 = -6, we need to multiply both sides of the equation by the same number. In this case, since we have x divided by -5 on the left side, we want to multiply by the reciprocal of -5 to eliminate the division.
To find the reciprocal, we simply flip the fraction. So the reciprocal of -5 is -1/5.
Now, we multiply both sides of the equation by -1/5:
(x/-5) * (-1/5) = -6 * (-1/5)
On the left side, the -5 in the numerator and the denominator cancel each other out, leaving just x:
x * (-1/5) = -6 * (-1/5)
Now we can simplify the equation:
-(1/5) * x = 6/5
To get x alone, we need to get rid of the coefficient -(1/5) in front of it. We can do this by multiplying both sides of the equation by the reciprocal of -(1/5), which is -5/1 or simply -5:
(-(1/5) * x) * (-5) = (6/5) * (-5)
Simplifying further:
(1/5) * x = -6
Now, we are left with x multiplied by (1/5) on the left side. To solve for x, we need to isolate it. We can achieve this by multiplying both sides of the equation by the reciprocal of (1/5), which is 5/1 or simply 5:
((1/5) * x) * 5 = -6 * 5
Simplifying once more:
x = -30
Therefore, the value of x that solves the equation x/-5 = -6 is x = -30.