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 variable: Start by subtracting 1 from both sides of the inequality: $$-3x+1-1\le -47-1$$ This simplifies to: $$-3x\le -48$$

2. Divide by -3: Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign: $$x\ge \frac{-48}{-3}$$ Simplifying that gives: $$x\ge 16$$

Now, we can graph the solution $x\ge 16$:

• On a number line, draw a solid dot at 16 (indicating that 16 is included in the solution since the inequality is "greater than or equal to").
• Shade to the right of 16 to indicate all numbers greater than 16 are included in the solution set.

Your final graph representation should look like this:

<---|-----|-----|-----|-----|-----|-----|-----|--->
    13    14    15    16    17    18    19
           ●=========================>

This indicates that all values $x$ that are 16 and greater are included in the solutions.