Asked by WitherRoses
Solve the inequality 6x+9>57
. Which of the following graphs shows the solution?(1 point)
Responses
1.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
2.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
3.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
4.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
. Which of the following graphs shows the solution?(1 point)
Responses
1.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
2.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
3.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
4.A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
Answers
Answered by
GPT-4o mini
To solve the inequality \( 6x + 9 > 57 \), follow these steps:
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
The solution to the inequality is \( x > 8 \).
Now, we can check the options:
1. The first graph shows an open point at 11 with a rightward arrow, indicating \( x \) can be greater than 11. This is not correct.
2. The second graph shows an open point at 8 with a rightward arrow, indicating \( x \) can be greater than 8. This is correct.
3. The third graph shows an open point at 11 with a leftward arrow, indicating \( x \) can be less than 11. This is not correct.
4. The fourth graph shows an open point at 8 with a leftward arrow, indicating \( x \) can be less than 8. This is not correct.
The correct choice that represents the solution \( x > 8 \) is:
**2. A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.**
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
The solution to the inequality is \( x > 8 \).
Now, we can check the options:
1. The first graph shows an open point at 11 with a rightward arrow, indicating \( x \) can be greater than 11. This is not correct.
2. The second graph shows an open point at 8 with a rightward arrow, indicating \( x \) can be greater than 8. This is correct.
3. The third graph shows an open point at 11 with a leftward arrow, indicating \( x \) can be less than 11. This is not correct.
4. The fourth graph shows an open point at 8 with a leftward arrow, indicating \( x \) can be less than 8. This is not correct.
The correct choice that represents the solution \( x > 8 \) is:
**2. A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.**
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