Question

simplify the equation: 1/2(4x - 1/3) = 2/3 options: x = 1/6; x = 3/4; x = 5/12; x = 2/5

Explanation:

Step1: Eliminate fraction by multiplying both sides by 2

Multiply both sides of the equation $\frac{1}{2}(4x - \frac{1}{3}) = \frac{2}{3}$ by 2 to get rid of the fraction on the left side.
$$2\times\frac{1}{2}(4x - \frac{1}{3}) = 2\times\frac{2}{3}$$
Simplify both sides: $4x - \frac{1}{3} = \frac{4}{3}$

Step2: Isolate the term with x

Add $\frac{1}{3}$ to both sides of the equation $4x - \frac{1}{3} = \frac{4}{3}$ to isolate the term with x.
$$4x - \frac{1}{3} + \frac{1}{3} = \frac{4}{3} + \frac{1}{3}$$
Simplify both sides: $4x = \frac{5}{3}$

Step3: Solve for x

Divide both sides of the equation $4x = \frac{5}{3}$ by 4 to solve for x.
$$x = \frac{5}{3} \div 4$$
Which is equivalent to $x = \frac{5}{3} \times \frac{1}{4} = \frac{5}{12}$

Answer:

x = 5/12 (the option with x = 5/12, which is the red-colored option in the image)