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

Question

(2 points)
Responses

Answer 1

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

1. Isolate the variable: Start by subtracting 1 from both sides of the inequality: \[ -3x + 1 - 1 \leq -47 - 1 \] This simplifies to: \[ -3x \leq -48 \]

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: \[ x \geq \frac{-48}{-3} \] Simplifying that gives: \[ x \geq 16 \]

Now, we can graph the solution \(x \geq 16\):

• 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.