Question

multiply both sides :multiply both sides by what?
$43(\square) = (10x + 19)(\square)$

Explanation:

Step1: Identify equality property

To keep the equation balanced, we use the multiplication property of equality, which states that multiplying both sides of an equation by the same non-zero value maintains equality.

Step2: Determine the multiplier

Any non-zero value works, but typically we use the same expression to isolate variables or simplify. The most logical choice is the same non-zero term for both blanks, often the reciprocal of a coefficient, but generally, any non-zero number or expression is valid. The standard choice to maintain balance is the same non-zero value, e.g., let the value be \(k\) where \(k
eq 0\). The most straightforward answer is the same non-zero expression, commonly \(\frac{1}{10x+19}\) (if \(10x+19
eq 0\)) to isolate 43, or any non-zero value. The simplest valid answer is the same non-zero number, such as 1, but the intended answer is likely the reciprocal of one side to solve for the other.

Answer:

The blanks can be filled with any non-zero value, most appropriately \(\boldsymbol{\frac{1}{10x+19}}\) (for \(10x
eq -19\)) in both boxes, or any identical non-zero number/expression. The simplest balanced choice is the same non-zero term, e.g., \(\frac{1}{10x+19}\) and \(\frac{1}{10x+19}\)