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. Subtract 1 from both sides: \[ -3x \leq -47 - 1 \] \[ -3x \leq -48 \]

2. 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:

1. On a number line, mark the point \(16\).
2. 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.
3. 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
        ●======================>

• 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.