N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
d–4≤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 \( d - 4 \leq 2 \), follow these steps:

1. Isolate the variable \( d \): \[ d - 4 \leq 2 \] Add 4 to both sides: \[ d \leq 2 + 4 \] \[ d \leq 6 \]

2. Graph the solution:

   • The solution \( d \leq 6 \) means that \( d \) can take any value less than or equal to 6.
   • On a number line, plot a closed dot at 6 (because 6 is included in the solution).
   • Draw a ray to the left from the closed dot to indicate that all values less than 6 are included in the solution.

Here is how the graph would look:

<---•======================>
     4      5      6      7

• The closed dot (•) at 6 represents that 6 is part of the solution, and the arrow to the left indicates all values less than 6 are also part of the solution.