N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
2≥h–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 \( 2 \geq h - 2 \), we will isolate \( h \).

1. Start with the inequality: \[ 2 \geq h - 2 \]

2. Add 2 to both sides to isolate \( h \): \[ 2 + 2 \geq h \] \[ 4 \geq h \] or equivalently, \[ h \leq 4 \]

This means that \( h \) can be any value less than or equal to 4.

Graphing the Solution

1. Endpoint: Since \( h \) can equal 4, we will use a closed dot on 4 to indicate that this value is included in the solution.

2. Ray: Since the solution encompasses all values less than 4, we will draw a ray (line with an arrow) extending to the left from the point 4.

Here is a step-by-step description on how to graph it:

• Place a closed dot on the number 4 on the number line.
• Draw an arrow extending to the left from the dot, indicating that all numbers to the left of 4 are part of the solution.

Final Graph Representation

Below is a text representation of the number line:

<---|------------------|------------------|-->
     2                  4                  6
                ●

• The dot at 4 is closed (●) indicating that 4 is included in the solution, and the arrow to the left signifies all numbers less than 4 are included in the solution.