Final answer:
To solve the equation 4(2x-3)=2(3x+1) algebraically, distribute and combine like terms to isolate the variable x. The solution is x = 7.
Step-by-step explanation:
To solve the algebraic equation 4(2x-3)=2(3x+1), first expand both sides:
8x - 12 = 6x + 2
Next, move the terms involving x to one side and the constant terms to the other side to isolate the variable:
8x - 6x = 2 + 12
2x = 14
Finally, divide both sides by 2 to solve for x:
x = 7
Remember that multiplication or division should apply to every term on either side of the equality. Solving an equation in one variable is a matter of isolating that variable, often through a series of algebraic steps that require careful checking and rechecking.