Graph the solutions for the inequality: -3x + 1<-47

1 answer

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

  1. Isolate the variable term:

    • Subtract 1 from both sides: \[ -3x < -47 - 1 \] \[ -3x < -48 \]
  2. Divide by -3:

    • Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign: \[ x > \frac{-48}{-3} \] \[ x > 16 \]

The solution to the inequality is \(x > 16\).

Graphing the Solution:

On a number line:

  • Draw a number line and mark the point at 16.
  • Since the inequality is \(x > 16\), you will use an open circle at 16 to indicate that 16 is not included in the solution.
  • Shade the line to the right of 16 to show that all numbers greater than 16 are part of the solution.

Here's a simple representation:

<---|----|----|----|----|----|----|----|----|----|--->
    10   11   12   13   14   15   16 (open circle)
                                               >

This graph indicates that all values greater than 16 are solutions to the inequality.