The answer is a = [tex]\frac{4}{-3}[/tex]
Step-by-step explanation:
1. Convert the mixed fraction to an improper fraction
To find the numerator, multiply the denominator by the whole number and add the numerator to it.
The denominator remains the same.
So, 2[tex]\frac{2}{3}[/tex] will be [tex]\frac{8}{3}[/tex]
2. Now the equation is,
[tex]\frac{3}{2}[/tex] a - [tex]\frac{4}{3}[/tex] a = [tex]\frac{10}{3}[/tex] + [tex]\frac{8}{3}[/tex] a
3. Take LCM on both sides.
For the left side, multiply the first fraction by [tex]\frac{3}{3}[/tex] and multiply the second fraction by [tex]\frac{2}{2}[/tex]
[tex]\frac{3*3}{2*3}[/tex] a - [tex]\frac{4*3}{3*3}[/tex] a = [tex]\frac{10+8a}{3}[/tex]
4. Solve by making a the subject
[tex]\frac{9a-8a}{6}[/tex] = [tex]\frac{10+8a}{3}[/tex]
[tex]\frac{a}{6}[/tex] = [tex]\frac{10+8a}{3}[/tex]
[tex]\frac{3a}{6}[/tex] =10+8a
[tex]\frac{a}{2}[/tex] = 10 + 8a
a = 2(10 + 8a)
a = 20 + 16a
a-16a = 20
-15a = 20
a = [tex]\frac{20}{-15}[/tex]
a = [tex]\frac{4}{-3}[/tex]
Therefore, the answer is a = [tex]\frac{4}{-3}[/tex]
Keyword: Equations
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