Solve for x: 2 over 3 (x − 2) = 4x

An equation is a mathematical statement with an 'equal to' symbol between two algebraic expressions that have equal values.

Answer: For 2 over 3 (x − 2) = 4x, x =(1 ± √2).

An equation is like a weighing balance with equal weights on both sides. If we add or subtract the same number from both sides of an equation, it still holds.

Explanation:

Multiply 3 (x − 2) on the both sides of the equation 2 over 3 (x − 2) = 4x

2/3 (x - 2) × 3 (x − 2) = 4x × 3 (x − 2)

2 = 4x × (3x − 6)

2 = 12x² - 24x

Subtract 2 from the both the sides of the equation 2 = 12x² - 24x

12x² - 24x - 2 = 0

Divide the both sides of the equation 12x² - 24x - 2 = 0 by 2

6x² - 12x - 1 = 0

Solving the above equation using quadratic equation formula,

Here, a = 6, b = -12, c = -1

x = { -(-12)  ± √[(-12) - 4(6)(-1)]} / 2(6) = [12  ± √(24)] / 12 = 1  ± √2

So, the solution of the equation 2 over 3 (x − 2) = 4x is x = (1 ± √2).