Answer:
−1.25 or -5/4
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