To graph the inequality \( x + 0.5 \geq 0.5 \) on a number line, follow these steps:
1. **Isolate \( x \) on one side of the inequality:**
\( x + 0.5 \geq 0.5 \)
Subtract 0.5 from both sides:
\( x \geq 0 \)
2. **Draw a number line:**
\[
\begin{aligned}
&--------------------------------------------------\\
&\quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad 2 \quad 3 \\
&--------------------------------------------------
\end{aligned}
\]
3. **Identify the point where \( x = 0 \):**
Since the inequality is \( x \geq 0 \), we mark the point 0. Use a closed circle to include the 0 because the inequality is "greater than or equal to."
4. **Shade the region where \( x \geq 0 \):**
Starting from the point 0, shade the number line to the right:
\[
\begin{aligned}
&--------------------------------------------------\\
&\quad -3 \quad -2 \quad -1 \quad \bullet \quad 1 \textcolor{blue}{\mathbf{\rightarrow}} \quad 2 \quad 3 \\
&----------------------------------------------------
\end{aligned}
\]
The arrow indicates that the region continues infinitely to the right.
So the solution to the inequality \( x + 0.5 \geq 0.5 \) is represented on the number line by a closed circle at 0 and shading to the right of 0.
x+0.5≥0.5 as a line graph
3 answers
can you make it more clear
Certainly! Let's clarify the steps with a more detailed and labeled number line:
1. **Isolate \( x \) on one side of the inequality:**
\[
x + 0.5 \geq 0.5
\]
Subtract 0.5 from both sides:
\[
x \geq 0
\]
2. **Draw a number line:**
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad 0 \quad \quad \quad \quad \quad 1 \quad \quad \quad \quad \quad 2 \quad \quad \quad \quad \quad 3 \\
&------------------------------------------------------------
\end{aligned}
\]
3. **Mark the point where \( x = 0 \):**
Since the inequality is \( x \geq 0 \), we use a closed circle at the point 0 to indicate that 0 is included in the solution set.
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad \mathbf{\bullet} \quad \quad \quad \quad \quad 1 \quad \quad \quad \quad \quad 2 \quad \quad \quad \quad \quad 3 \\
&------------------------------------------------------------
\end{aligned}
\]
4. **Shade the region where \( x \geq 0 \):**
Starting from the point 0, shade the number line to the right, indicating that all numbers greater than or equal to 0 are included.
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad \mathbf{\bullet} \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 1 \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 2 \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 3 \quad \\
&------------------------------------------------------------
\end{aligned}
\]
Let's break it down step-by-step visually:
- The closed circle (●) at 0 shows that \( x \) can be exactly 0.
- The arrow (→) to the right of 0 shows that \( x \) can be any value greater than 0.
This means the solution to the inequality \( x + 0.5 \geq 0.5 \) is all the numbers starting from 0 and extending to the right indefinitely.
1. **Isolate \( x \) on one side of the inequality:**
\[
x + 0.5 \geq 0.5
\]
Subtract 0.5 from both sides:
\[
x \geq 0
\]
2. **Draw a number line:**
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad 0 \quad \quad \quad \quad \quad 1 \quad \quad \quad \quad \quad 2 \quad \quad \quad \quad \quad 3 \\
&------------------------------------------------------------
\end{aligned}
\]
3. **Mark the point where \( x = 0 \):**
Since the inequality is \( x \geq 0 \), we use a closed circle at the point 0 to indicate that 0 is included in the solution set.
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad \mathbf{\bullet} \quad \quad \quad \quad \quad 1 \quad \quad \quad \quad \quad 2 \quad \quad \quad \quad \quad 3 \\
&------------------------------------------------------------
\end{aligned}
\]
4. **Shade the region where \( x \geq 0 \):**
Starting from the point 0, shade the number line to the right, indicating that all numbers greater than or equal to 0 are included.
\[
\begin{aligned}
&\quad \quad -3 \quad \quad \quad \quad \quad -2 \quad \quad \quad \quad \quad -1 \quad \quad \quad \quad \quad \mathbf{\bullet} \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 1 \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 2 \textcolor{blue}{\mathbf{\rightarrow}} \quad \quad \quad \quad \quad 3 \quad \\
&------------------------------------------------------------
\end{aligned}
\]
Let's break it down step-by-step visually:
- The closed circle (●) at 0 shows that \( x \) can be exactly 0.
- The arrow (→) to the right of 0 shows that \( x \) can be any value greater than 0.
This means the solution to the inequality \( x + 0.5 \geq 0.5 \) is all the numbers starting from 0 and extending to the right indefinitely.