Solve for x:
-5/(2 x) = -5/6-7/(4 x)
-5/(2 x) = -5/(2 x) and -5/6-7/(4 x) = -5/6-7/(4 x):
-5/(2 x) = -5/6-7/(4 x)
Bring -5/6-7/(4 x) together using the common denominator 12 x:
-5/(2 x) = (-21-10 x)/(12 x)
Cross multiply:
-60 x = 2 x (-21-10 x)
Expand out terms of the right hand side:
-60 x = -42 x-20 x^2
Add 20 x^2+42 x to both sides:
20 x^2-18 x = 0
Factor x and constant terms from the left hand side:
2 x (10 x-9) = 0
Divide both sides by 2:
x (10 x-9) = 0
Split into two equations:
x = 0 or 10 x-9 = 0
Add 9 to both sides:
x = 0 or 10 x = 9
Divide both sides by 10:
x = 0 or x = 9/10
-5/(2 x) => -5/(2 0) = infinity^~
-5/6-7/(4 x) => -7/(4 0)-5/6 = infinity^~:
So this solution is incorrect
-5/(2 x) => -5/((2 9)/10) = -25/9
-5/6-7/(4 x) => -5/6-7/((4 9)/10) = -25/9:
So this solution is correct
The solution is:
Answer: | x = 9/10
-5/2x = -7/4x-5/6
Solve for x:
(-5 x)/2 = -5/6-(7 x)/4
Put each term in -5/6-(7 x)/4 over the common denominator 12: -5/6-(7 x)/4 = (-10)/12-(21 x)/12:
(-5 x)/2 = (-10)/12-(21 x)/12
(-10)/12-(21 x)/12 = (-10-21 x)/12:
(-5 x)/2 = (-10-21 x)/12
Multiply both sides by 12:
(-5×12 x)/2 = (12 (-10-21 x))/12
12/2 = (2×6)/2 = 6:
-56 x = (12 (-10-21 x))/12
(12 (-10-21 x))/12 = 12/12×(-10-21 x) = -10-21 x:
-5×6 x = -10-21 x
6 (-5) = -30:
-30 x = -10-21 x
Add 21 x to both sides:
21 x-30 x = (21 x-21 x)-10
21 x-21 x = 0:
21 x-30 x = -10
21 x-30 x = -9 x:
-9 x = -10
Divide both sides of -9 x = -10 by -9:
(-9 x)/(-9) = (-10)/(-9)
(-9)/(-9) = 1:
x = (-10)/(-9)
The sign of (-10)/(-9) is positive, so (-10)/(-9) = 1×10/9:
Answer: | x = 10/9
+1904 Look at my answer. 10/9 is not the correct answer. The answer is 9/10 or 0.9.
+1904 \(\frac{-5}{2x}=\frac{-7}{4x}-\frac{5}{6}\)
\(-\frac{5}{2x}=-\frac{7}{4x}-\frac{5}{6}\)
\((-\frac{5}{2x})\times4x=(-\frac{7}{4x}-\frac{5}{6})\times4x\)
\(-\frac{20x}{2x}=(-\frac{7}{4x}-\frac{5}{6})\times4x\)
\(-\frac{20x}{2x}=-\frac{28x}{4x}-\frac{20x}{6}\)
\(-10=-\frac{28x}{4x}-\frac{20x}{6}\)
\(-10=-7-\frac{20x}{6}\)
\(-10\times6=(-7-\frac{20x}{6})\times6\)
\(-60=(-7-\frac{20x}{6})\times6\)
\(-60=-42-\frac{120x}{6}\)
\(-60=-42-20x\)
\(-60+42=-42-20x+42\)
\(-18=-42-20x+42\)
\(-18=0-20x\)
\(-18=-20x\)
\(\frac{-18}{-20}=\frac{-20x}{-20}\)
\(\frac{9}{10}=\frac{-20x}{-20}\)
\(\frac{9}{10}=\frac{1x}{1}\)
\(\frac{9}{10}=\frac{x}{1}\)
\(\frac{9}{10}=x\)
\(0.9=x\)
\(x=0.9\)
.Solve for x:
-5/(2 x) = -5/6-7/(4 x)
-5/(2 x) = -5/(2 x) and -5/6-7/(4 x) = -5/6-7/(4 x):
-5/(2 x) = -5/6-7/(4 x)
Bring -5/6-7/(4 x) together using the common denominator 12 x:
-5/(2 x) = (-21-10 x)/(12 x)
Cross multiply:
-60 x = 2 x (-21-10 x)
Expand out terms of the right hand side:
-60 x = -42 x-20 x^2
Add 20 x^2+42 x to both sides:
20 x^2-18 x = 0
Factor x and constant terms from the left hand side:
2 x (10 x-9) = 0
Divide both sides by 2:
x (10 x-9) = 0
Split into two equations:
x = 0 or 10 x-9 = 0
Add 9 to both sides:
x = 0 or 10 x = 9
Divide both sides by 10:
x = 0 or x = 9/10
-5/(2 x) => -5/(2 0) = infinity^~
-5/6-7/(4 x) => -7/(4 0)-5/6 = infinity^~:
So this solution is incorrect
-5/(2 x) => -5/((2 9)/10) = -25/9
-5/6-7/(4 x) => -5/6-7/((4 9)/10) = -25/9:
So this solution is correct
The solution is:
Answer: | x = 9/10
+1904 In order to add or subtract fractions the numerators have to be the same bfore you can add or subtract. The actual answer is x=9/10 or x=0.9.
