Answer:
See the three answers with their explanation below
Explanation:
a. To eliminate the fraction from each side you multiply both sides by the least common denominator of the fractions of the two sides.
In this case it is 2×3 = 6
See how you do it:
[tex]6\times \frac{1}{2}(x-4)=6\times \frac{1}{3}x+6\times 2\\ \\ 3(x-4)=2x+12[/tex]
b. This word problem would lead to the given equation:
Half the age of Alice 4 years ago equals 2 more than one third of her current age.
- Current age: x
- Age four years ago: x - 4
- Half the age of Alice four years ago: [tex]\frac{1}{2}(x-4)[/tex]
- 2 more than one third of her current age: [tex]2+\frac{1}{3}x=\frac{1}{3}x+2[/tex]
Equality condition:
- [tex]\frac{1}{2}(x-4)=\frac{1}{3}x+2[/tex]
c. Solution
[tex]\frac{1}{2}(x-4)=\frac{1}{3}x+2\\ \\ 3(x-4)=2x+12\\ \\ 3x-12=2x+12\\ \\ x=24[/tex]
Meaning: Alice is currently 24 years old.
