To solve the inequality \(-3x + 1 < -47\), follow these steps:
-
Isolate the variable term:
- Subtract 1 from both sides: \[ -3x < -47 - 1 \] \[ -3x < -48 \]
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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.