To solve the inequality \(-3x + 1 \leq -47\), follow these steps:
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Subtract 1 from both sides: \[ -3x \leq -47 - 1 \] \[ -3x \leq -48 \]
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Divide both sides by -3. Remember that when you divide or multiply by a negative number, you must flip the inequality sign: \[ x \geq \frac{-48}{-3} \] \[ x \geq 16 \]
Graphing the Solution:
- On a number line, mark the point \(16\).
- Since the inequality is \(x \geq 16\), you will use a closed dot at \(16\) to indicate that \(16\) is included in the solution set.
- Shade the line to the right of the dot to represent all values greater than \(16\).
Here’s a simple representation:
<---|---|---|---|---|---|---|---|---|---|--->
15 16 17 18 19
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- The closed dot (●) indicates that \(16\) is included, and the shading to the right indicates that all values greater than \(16\) are part of the solution.