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

Question

(2 points)
Responses

Answer 1

To solve the inequality $-3x+1\le -47$, follow these steps:

1. Isolate the term with $x$: $$-3x+1\le -47$$ Subtract 1 from both sides: $$-3x\le -48$$

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: $$x\ge 16$$

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.