Question

does the equation 12 = 2x have one solution, no solutions, or infinitely many solutions?
divide both sides of the equation by 2 to find the value of x.
12/2 = 2x/2
6 = blank

Explanation:

Step1: Simplify the right - hand side

We have the equation \(\frac{12}{2}=\frac{2x}{2}\). First, calculate \(\frac{2x}{2}\). According to the rule of dividing a term with a variable by a non - zero number, \(\frac{2x}{2}=x\) (because when we divide \(2x\) by \(2\), the \(2\)'s cancel out, leaving \(x\)). And we know that \(\frac{12}{2} = 6\).

Step2: Determine the solution of the equation

From the simplification in Step 1, we get \(6=x\), which means \(x = 6\). Since we can find a unique value for \(x\) that satisfies the equation \(12 = 2x\), the equation has one solution. And the value in the box (from the simplification of \(\frac{2x}{2}\)) is \(x\) (or when we consider the value of \(x\), it is \(6\), but in the context of the box in the given calculation, after dividing \(\frac{2x}{2}\), we get \(x\), and since \(6=x\), the value in the box is \(x\) (or \(6\) when we substitute the value of \(x\)). But for the equation's solution type, since we have a unique \(x = 6\), the equation has one solution.

Answer:

The equation \(12 = 2x\) has one solution, and the value in the box is \(x\) (or \(6\) as \(x = 6\)). The equation has one solution.