N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
6≤d–2
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \( 6 \leq d - 2 \), we can follow these steps:

1. Isolate the variable \( d \): \[ 6 \leq d - 2 \] Add 2 to both sides: \[ 6 + 2 \leq d \] Simplifying this gives: \[ 8 \leq d \] or equivalently, \[ d \geq 8 \]

2. Graph the solution:

   • Since the inequality is \( d \geq 8 \), this means that the solution includes \( d = 8 \) and all values greater than 8.
   • On a number line, you will plot the point \( 8 \).
   • Since it includes \( 8 \) (the inequality is "greater than or equal to"), you will use a closed dot at \( 8 \).
   • From the point \( 8 \), draw a ray extending to the right (toward positive infinity).

Graph representation

• A closed dot at 8
• A ray extending right from 8

Visual Representation:

  <---|---|---|---|---|---|---|---|---|---|---|---|---|--->
       5   6   7   ●   9   10  11
               8

In this representation, the closed dot at 8 indicates that 8 is included in the solution, and the arrow indicates that all values greater than 8 are also included in the solution set.