Question
Solve the inequality x/8≥1/2
. Which of the following graphs shows the solution?(1 point)
Responses
An illustration shows a number line ranging from negative 10 to 10 in increments of 1. An open circle is plotted at 4. A rightward arrow is drawn on the number line originating at the open circle and going beyond 10.
Image with alt text: An illustration shows a number line ranging from negative 10 to 10 in increments of 1. An open circle is plotted at 4. A rightward arrow is drawn on the number line originating at the open circle and going beyond 10.
An illustration shows a number line ranging from negative 3 to 3 in increments of 1. A closed circle is plotted just to the right of 0. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 3.
Image with alt text: An illustration shows a number line ranging from negative 3 to 3 in increments of 1. A closed circle is plotted just to the right of 0. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 3.
An illustration shows a number line ranging from 0 to 20 in increments of 1. A closed circle is plotted at 16. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 20.
Image with alt text: An illustration shows a number line ranging from 0 to 20 in increments of 1. A closed circle is plotted at 16. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 20.
An illustration shows a number line ranging from negative 10 to 10 in increments of 1. A closed circle is plotted at 4. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 10.
. Which of the following graphs shows the solution?(1 point)
Responses
An illustration shows a number line ranging from negative 10 to 10 in increments of 1. An open circle is plotted at 4. A rightward arrow is drawn on the number line originating at the open circle and going beyond 10.
Image with alt text: An illustration shows a number line ranging from negative 10 to 10 in increments of 1. An open circle is plotted at 4. A rightward arrow is drawn on the number line originating at the open circle and going beyond 10.
An illustration shows a number line ranging from negative 3 to 3 in increments of 1. A closed circle is plotted just to the right of 0. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 3.
Image with alt text: An illustration shows a number line ranging from negative 3 to 3 in increments of 1. A closed circle is plotted just to the right of 0. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 3.
An illustration shows a number line ranging from 0 to 20 in increments of 1. A closed circle is plotted at 16. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 20.
Image with alt text: An illustration shows a number line ranging from 0 to 20 in increments of 1. A closed circle is plotted at 16. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 20.
An illustration shows a number line ranging from negative 10 to 10 in increments of 1. A closed circle is plotted at 4. A rightward arrow is drawn on the number line originating at the closed circle and going beyond 10.
Answers
Answered by
GPT-4o mini
To solve the inequality \( \frac{x}{8} \geq \frac{1}{2} \), we first multiply both sides by 8 to eliminate the fraction:
\[
x \geq \frac{1}{2} \cdot 8
\]
Calculating the right side gives:
\[
x \geq 4
\]
Now, this means that the solution set includes all values of \( x \) that are greater than or equal to 4. On a number line, this will be represented by a closed circle at 4 (to indicate that 4 is included in the solution set) with an arrow pointing to the right (to indicate all values greater than 4).
Looking at the options provided:
1. An open circle at 4 with a rightward arrow (incorrect, because 4 should be included.)
2. A closed circle just to the right of 0 with a rightward arrow (incorrect, since it doesn't start at 4.)
3. A closed circle at 16 with a rightward arrow (incorrect, since it starts at 16.)
4. A closed circle at 4 with a rightward arrow (correct, because it includes 4 and goes to infinity.)
Thus, the correct response is the option showing a closed circle at 4 with a rightward arrow.
\[
x \geq \frac{1}{2} \cdot 8
\]
Calculating the right side gives:
\[
x \geq 4
\]
Now, this means that the solution set includes all values of \( x \) that are greater than or equal to 4. On a number line, this will be represented by a closed circle at 4 (to indicate that 4 is included in the solution set) with an arrow pointing to the right (to indicate all values greater than 4).
Looking at the options provided:
1. An open circle at 4 with a rightward arrow (incorrect, because 4 should be included.)
2. A closed circle just to the right of 0 with a rightward arrow (incorrect, since it doesn't start at 4.)
3. A closed circle at 16 with a rightward arrow (incorrect, since it starts at 16.)
4. A closed circle at 4 with a rightward arrow (correct, because it includes 4 and goes to infinity.)
Thus, the correct response is the option showing a closed circle at 4 with a rightward arrow.
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