How do you solve 19/24=-5/6x-1/4 step by step, with verification?

−1.25 or -5/4

Step-by-step explanation:

Equation

19/24 = -5/6x - 1/4

first swap sides so that all variable terms are on the left hand side

-5/6x - 1/4 = 19/24

add 1/4 to both sides.

-5/6x = 19/24 + 1/4

Least common multiple of 24 and 4 is 24. Convert 19/24 and 1/4 to fractions with a denominator of 24.

-5/6x = 19/24 + 6/24

Since 19/24 and 6/24 have the same denominator, add them by adding their numerators.

-5/6x = 19+6/24

Add 19 and 6 to get 25

-5/6x = 25/24

Multiply both sides by -6/5, the reciprocal of -5/6

x = 25/24 (-6/5)

Multiply 25/24 times -6/5 by multiplying numerator times numerator and denominator times denominator.

x = 25(-6) / 24x5

Do the multiplications in the fraction 25(-6) / 24x5

x = -150/120

Reduce the fraction -150/120 to the lowest terms by extracting and canceling out 30

x = -5/4

With verification

First write the equation and our value for x

19/24 = -5/6x - 1/4

x = -5/4

swap sides so that all variable terms are on the left hand side

-5/6x - 1/4 = 19/24

convert -5/6x to have the same denominator of 19/24.

-5 (4)

-6 (4)

== -20/24x

write the full equation with the converted variable

-20/24x - 1/4 = 19/24

Convert 1/4 to have the same denominator of 19/24

1 (6)

4 (6)

== 6/24

write the full equation with the converted variable and retain the minus sign

-20/24x - 6/24 = 19/24

write our value of X

-5/4

convert x to have the same denominator of -20/24x

-5(6)

-4(6)

= -30/24

x = -30/24

replace x in -20/24x with our updated value of x

-20/24(-30/24)

Multiply -20/24 by -30/24

= 25/24

write the full equation

25/24 - 6/24 = 19/24

subtract 25/24 by 6/24

19/24 = 19/24

the fraction 19/24 is equal to 19/24

verification complete

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours