Question

consider the equation $w - 3 = w$.
what do you know about the expressions on each side of the equation?
the value of $w + 3$ is always
more than the value of $w$.
that means the value of $w + 3$ will equal the value of $w$.

Explanation:

Step1: Analyze the difference between \(x + 3\) and \(x\)

Let's find the difference \((x + 3)-x\). Using the distributive property of subtraction over addition \((x + 3)-x=x - x+3\). Since \(x - x = 0\), we have \((x + 3)-x=3\). So the value of \(x + 3\) is always \(3\) more than the value of \(x\).

Step2: Determine the equality of \(x + 3\) and \(x\)

If \(x+3=x\), then subtracting \(x\) from both sides gives \(3 = 0\), which is a contradiction. So the value of \(x + 3\) will never equal the value of \(x\).

Answer:

The first blank is \(3\), and the second blank is "never".