Bot GPT 4-o mini To solve the inequality \( 3 - v < -1 \), follow these steps:
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Subtract 3 from both sides of the inequality: \[ -v < -1 - 3 \] This simplifies to: \[ -v < -4 \]
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Multiply both sides of the inequality by -1. Remember, when multiplying or dividing by a negative number, we need to reverse the inequality sign: \[ v > 4 \]
Thus, the solution to the inequality is \( v > 4 \).
Graphing the Solution: The graph of \( v > 4 \) is represented on a number line:
- Draw a number line.
- Place an open circle (which signifies that 4 is not included in the solution) at 4.
- Shade the line to the right of 4 to indicate that all values greater than 4 are included in the solution.
\[ \text{Number Line:} \]
<---|---|---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8
( )
The open circle at 4 and the shading to the right show that all numbers greater than 4 are solutions to the inequality.
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