Question

Please help me , I have been try to solve it for 2 hours. thank you very much. ​

Answer 1

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:

$6\times \frac{1}{2}(x-4)=6\times \frac{1}{3}x+6\times 2\\ \\ 3(x-4)=2x+12$

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:  $\frac{1}{2}(x-4)$

• 2 more than one third of her current age: $2+\frac{1}{3}x=\frac{1}{3}x+2$

Equality condition:

• $\frac{1}{2}(x-4)=\frac{1}{3}x+2$

c. Solution

$\frac{1}{2}(x-4)=\frac{1}{3}x+2\\ \\ 3(x-4)=2x+12\\ \\ 3x-12=2x+12\\ \\ x=24$

Meaning: Alice is currently 24 years old.