Question

Determine which symbol can replace the ? to make the following an the following an equation: 1/2x ? 1/3x -5
A. +
B. *
C. =
D. /

Answer 1

To determine which symbol can replace "?" to make the equation valid, we need to analyze the expression \( \frac{1}{2}x \, ? \, \frac{1}{3}x - 5 \).

Let's list out the options:

A. +
B. *
C. =
D. /

### Option A: +
If we use the plus sign:
\[
\frac{1}{2}x + \frac{1}{3}x - 5
\]
This is a valid mathematical expression, but we don't know if it equals something specific without further information.

### Option B: *
If we use the multiplication sign:
\[
\frac{1}{2}x * \frac{1}{3}x - 5
\]
This also forms a valid expression, but again we don't know if it equals something specific.

### Option C: =
Using the equal sign:
\[
\frac{1}{2}x = \frac{1}{3}x - 5
\]
This forms an equation that can be solved.

### Option D: /
Using the division sign:
\[
\frac{1}{2}x / \frac{1}{3}x - 5
\]
This will also form a valid expression but might not mean anything specific.

Now let's analyze option C further:
\[
\frac{1}{2}x = \frac{1}{3}x - 5
\]
To solve it:
1. Rearranging gives:
\[
\frac{1}{2}x - \frac{1}{3}x = -5
\]
2. Finding a common denominator (which is 6):
\[
\frac{3}{6}x - \frac{2}{6}x = -5
\]
3. This simplifies to:
\[
\frac{1}{6}x = -5
\]
4. Multiplying both sides by 6 gives:
\[
x = -30
\]

This shows that using "=" makes a valid equation.

### Conclusion:
The symbol that can replace "?" to make the expression a valid equation is:

**C. =**