solve the inequality then put it on a numberline

Question

2z–3≥1

Answer 1

To solve the inequality \( 2z - 3 \geq 1 \), follow these steps:

1. Add 3 to both sides: \[ 2z - 3 + 3 \geq 1 + 3 \] This simplifies to: \[ 2z \geq 4 \]

2. Divide both sides by 2: \[ \frac{2z}{2} \geq \frac{4}{2} \] This simplifies to: \[ z \geq 2 \]

Now that we have the solution \( z \geq 2 \), we can represent it on a number line.

Number Line Representation:

• Draw a horizontal line to represent the number line.
• Mark a point for 2 on the line.
• Since the inequality is \( z \geq 2 \), we use a closed circle (●) on 2 to indicate that it is included in the solution.
• Shade the region to the right of 2 to represent all values greater than or equal to 2.

Here is a textual representation:

<---|---|---|---|---|---|---|---|---|---|--->
    0   1   2   3   4   5   6   7   8   9
          ●================>

The closed circle at 2 indicates \( z = 2 \) is included, and the shading extends infinitely to the right, indicating all numbers greater than 2 are part of the solution.