Final answer:
To find the value of x in the equation 1/2 * (20 - x) = 2/3, solve for x through multiplication and division to simplify the terms, resulting in x ≈ 18.67.
Step-by-step explanation:
In order to find the value of the variable in the equation 1/2 * (20 - x) = 2/3, we can solve the equation step-by-step.
- First, simplify the equation by multiplying both sides by 2 to get rid of the fraction: (20 - x) = (2/3) * 2.
- Next, multiply the fractions: (20 - x) = 4/3.
- Now, subtract 20 from both sides of the equation: -x = 4/3 - 20.
- Simplify the right side of the equation: -x = (4/3) - (60/3) = -56/3.
- Finally, divide both sides of the equation by -1 to solve for x: x = 56/3.
Therefore, the value of the variable x in the equation 1/2 * (20 - x) = 2/3 is 56/3 or 18.67.