Respuesta :
The value of "a" is a = -1.25 or [tex]\frac{-5}{4}[/tex]
Solution:
Given expression is:
[tex]\frac{1}{3}a - \frac{1}{4} = \frac{5}{6} - \frac{3}{2}[/tex]
We have to solve the above expression for "a"
[tex]\frac{a}{3} - \frac{1}{4} = \frac{5}{6} - \frac{3}{2}[/tex]
Take L.C.M of denominators of L.H.S and R.H.S
L.C.M of 3 and 4:
List all prime factors for each number.
Prime factor of 3 = 3
Prime factor of 4 = 2 x 2
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 3
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 = 12
L.C.M of 6 and 2:
Prime factor of 6 = 2 x 3
Prime factor of 2 = 2
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3
Multiply these factors together to find the LCM.
LCM = 2 x 3 = 6
Now make the denominators same
[tex]\frac{a}{3} - \frac{1}{4} = \frac{5}{6} - \frac{3}{2}\\\\\frac{a \times 4}{3 \times 4} - \frac{1 \times 3}{4 \times 3} = \frac{5 \times 1}{6 \times 1} - \frac{3 \times 3}{2 \times 3}\\\\\frac{4a}{12}-\frac{3}{12} = \frac{5}{6}-\frac{9}{6}\\\\\frac{4a - 3}{12} = \frac{5-9}{6}[/tex]
Simplify the above expression
[tex]\frac{4a - 3}{12} = \frac{5-9}{6}\\\\4a - 3 = 2(-4)\\\\4a - 3 = -8\\\\4a = -8 + 3\\\\4a = -5\\\\a = \frac{-5}{4}[/tex]
Thus value of "a" is a = -1.25 or [tex]\frac{-5}{4}[/tex]
