Question
Solve the inequality 6x+9>57 . Which of the following graphs shows the solution?(1 point)
all 4 number line start from positive 18 and end at negative 2
the first number line is dotted from negative 2 and down to 8
the second number line is dotted from positive 18 down to positive 8
the third number line is dotted from positive 18 down to positive 11
the last number line is dotted from negative 2 all the way to positive 11
pls choose one or pick the closest option
all 4 number line start from positive 18 and end at negative 2
the first number line is dotted from negative 2 and down to 8
the second number line is dotted from positive 18 down to positive 8
the third number line is dotted from positive 18 down to positive 11
the last number line is dotted from negative 2 all the way to positive 11
pls choose one or pick the closest option
Answers
Answered by
GPT-4o mini
To solve the inequality \(6x + 9 > 57\), we can first isolate \(x\).
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Now, divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
Therefore, the solution to the inequality is \(x > 8\).
Now we can analyze the options for the number line:
- We are looking for a graph that shows \(x\) values greater than 8, which means the line should start above 8 and extend to the right.
Among the options given, the first number line starts at \(-2\) and goes up to \(8\), which does not show values greater than 8.
The second number line starts at \(18\) and goes down to \(8\), which indicates values less than or equal to \(8\), so it is not a solution.
The third number line starts at \(18\) and goes down to \(11\), which also does not include values above \(8\).
The last number line starts at \(-2\) and goes up to \(11\) but does not show an open interval starting from \(8\) extending to the right.
However, since none of the options clearly represent the \(x > 8\) solution, the second option (starting from \(18\) going down to \(8\)) is the closest, even though it does not accurately reflect the solution of the inequality.
If you are forced to pick the "closest" based on the options given, select the second one.
If you have the opportunity, best representation would be a number line starting at \(8\) with an open dot (indicating \(8\) is not included) and extending to the right.
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Now, divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
Therefore, the solution to the inequality is \(x > 8\).
Now we can analyze the options for the number line:
- We are looking for a graph that shows \(x\) values greater than 8, which means the line should start above 8 and extend to the right.
Among the options given, the first number line starts at \(-2\) and goes up to \(8\), which does not show values greater than 8.
The second number line starts at \(18\) and goes down to \(8\), which indicates values less than or equal to \(8\), so it is not a solution.
The third number line starts at \(18\) and goes down to \(11\), which also does not include values above \(8\).
The last number line starts at \(-2\) and goes up to \(11\) but does not show an open interval starting from \(8\) extending to the right.
However, since none of the options clearly represent the \(x > 8\) solution, the second option (starting from \(18\) going down to \(8\)) is the closest, even though it does not accurately reflect the solution of the inequality.
If you are forced to pick the "closest" based on the options given, select the second one.
If you have the opportunity, best representation would be a number line starting at \(8\) with an open dot (indicating \(8\) is not included) and extending to the right.
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