Question
Solve the inequality 6x+9>57 . Which of the following graphs shows the solution?(1 point)
all 4 graphs are marked from positive 18 all the way down to 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
all 4 graphs are marked from positive 18 all the way down to 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
Answers
Answer
wrong one of these are correct
Answered by
GPT-4o mini
To solve the inequality \(6x + 9 > 57\), we first need to isolate \(x\):
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Now, divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
Thus, the solution to the inequality is \(x > 8\).
Now, we can analyze the graph options provided:
1. **Graph 1**: Dotted from \(-2\) down to \(8\) (not a solution).
2. **Graph 2**: Dotted from \(18\) down to \(8\) (not a solution).
3. **Graph 3**: Dotted from \(18\) down to \(11\) (not a solution).
4. **Graph 4**: Dotted from \(-2\) all the way to \(11\) (not a solution).
None of the descriptions of the graphs provided indicate a correct representation of the solution \(x > 8\). A correct graph would show a dotted line starting at \(8\) and extending to the right towards positive infinity.
If this graph is not explicitly listed in your options, please verify or check for alternative options.
1. Subtract 9 from both sides:
\[
6x > 57 - 9
\]
\[
6x > 48
\]
2. Now, divide both sides by 6:
\[
x > \frac{48}{6}
\]
\[
x > 8
\]
Thus, the solution to the inequality is \(x > 8\).
Now, we can analyze the graph options provided:
1. **Graph 1**: Dotted from \(-2\) down to \(8\) (not a solution).
2. **Graph 2**: Dotted from \(18\) down to \(8\) (not a solution).
3. **Graph 3**: Dotted from \(18\) down to \(11\) (not a solution).
4. **Graph 4**: Dotted from \(-2\) all the way to \(11\) (not a solution).
None of the descriptions of the graphs provided indicate a correct representation of the solution \(x > 8\). A correct graph would show a dotted line starting at \(8\) and extending to the right towards positive infinity.
If this graph is not explicitly listed in your options, please verify or check for alternative options.