Question

Determine which symbol can replace the ? to make the following an equation:

1/2x ? 1/3x−5


(1 point)
Responses

÷
divided by

⋅
times

+
plus

=

Answer 1

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

Given the expression, we want to find what operation between \( \frac{1}{2}x \) and \( \frac{1}{3}x - 5 \) makes the equation valid.

1. **If we use "+" (plus)**:
\[
\frac{1}{2}x + \left(\frac{1}{3}x - 5\right) = \frac{1}{2}x + \frac{1}{3}x - 5
\]
This simplifies to \( \left(\frac{3}{6}x + \frac{2}{6}x\right) - 5 = \frac{5}{6}x - 5\).

2. **If we use "−" (minus)**:
\[
\frac{1}{2}x - \left(\frac{1}{3}x - 5\right) = \frac{1}{2}x - \frac{1}{3}x + 5
\]
This simplifies to \( \left(\frac{3}{6}x - \frac{2}{6}x\right) + 5 = \frac{1}{6}x + 5\).

3. **If we use "⋅" (times)**:
\[
\frac{1}{2}x \cdot \left(\frac{1}{3}x - 5\right)
\]
This would result in a product, which does not seem to relate easily.

4. **If we use "÷" (divided by)**:
\[
\frac{1}{2}x ÷ \left(\frac{1}{3}x - 5\right)
\]
This would activate a division which also does not easily relate.

Since we seem to be looking for an operation that connects the two expressions in a meaningful equation, the addition sign \( + \) appears most logical as it combines two terms to form a linear expression.

Thus, the correct answer to replace the "?" is:

**+ (plus)**.