Which graph represents the solution of the inequality x subtracted from 7 is less than 2

Options

A.
B.
C.
D.

Answer

To solve the inequality "x subtracted from 7 is less than 2", we can express this mathematically as:

1. **Write the inequality**:
The phrase "x subtracted from 7" can be written as \( 7 - x < 2 \).

2. **Rearrange the inequality**:
To isolate \( x \), we can first subtract 7 from both sides:
\[ 7 - x < 2 \implies -x < 2 - 7 \]
Simplifying the right side gives:
\[ -x < -5 \]

3. **Multiply by -1**:
When we multiply or divide an inequality by a negative number, we must reverse the inequality sign:
\[ x > 5 \]

4. **Interpret the solution**:
The solution \( x > 5 \) means that \( x \) can take any value greater than 5.

5. **Graph the solution**:
On a number line, we would represent this by drawing an open circle at 5 (indicating that 5 is not included in the solution) and shading to the right of 5 to indicate all numbers greater than 5.

6. **Identify the correct graph**:
From the options provided, we look for a graph that has an open circle at 5 and shading to the right.