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8. Graph the solutions for the inequality: −3x+1≤−47

(2 points)
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To solve the inequality \(-3x + 1 \leq -47\), follow these steps:

  1. Isolate the term with \(x\): \[ -3x + 1 \leq -47 \] Subtract 1 from both sides: \[ -3x \leq -48 \]

  2. Solve for \(x\): Divide both sides by -3. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign: \[ x \geq 16 \]

  3. Graph the solution: On a number line:

    • Draw a number line.
    • Place a solid circle at 16 (indicating that 16 is included in the solution).
    • Shade the line to the right of 16 to indicate that all numbers greater than or equal to 16 are included in the solution.

Here's a description of how you would represent this graphically:

  • Number line:
------|------|------|------|------|------|------|------|------|------
     14     15     16     17     18     19     20     21     22
             ●======================>

In this graph, the solid dot at 16 indicates that 16 is part of the solution, and the arrow indicates that all values greater than 16 are also included.