Question

does the equation 4(x - 2) = 4x - 6 have one solution, no solutions, or infinitely many solutions? keeping the equation balanced? 4(x - 2) = 4x - 6 4(x - 2) = 4x - 8 subtract 4x from each side multiply each side by 4x add 4x to each side

Explanation:

Step1: Expand left-hand side

$4(x-2) = 4x - 8$

Step2: Set equal to right-hand side

$4x - 8 = 4x - 6$

Step3: Subtract $4x$ from both sides

$4x - 8 - 4x = 4x - 6 - 4x$
$-8 = -6$

Answer:

The equation has no solutions, because simplifying leads to a false statement ($-8=-6$) that can never be true for any value of $x$. The correct balancing step is "Subtract 4x from each side".