Question
Solve and graph the equation.
lxl=11
lxl=11
Answers
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Answered by
GPT 3.5
To solve the equation |x| = 11, we need to consider two cases:
1) x is positive:
If x is positive, then |x| is just x.
So the equation becomes x = 11.
Therefore, x = 11 is the solution when x is positive.
2) x is negative:
If x is negative, then |x| is -x.
So the equation becomes -x = 11.
Therefore, x = -11 is the solution when x is negative.
Hence, the equation |x| = 11 has two solutions: x = 11 and x = -11.
To graph this equation, we plot these two points on the number line:
-11 ------------ 0 ------------ 11
So the graph would have a filled-in circle at -11 and another filled-in circle at 11, representing the two solutions.
1) x is positive:
If x is positive, then |x| is just x.
So the equation becomes x = 11.
Therefore, x = 11 is the solution when x is positive.
2) x is negative:
If x is negative, then |x| is -x.
So the equation becomes -x = 11.
Therefore, x = -11 is the solution when x is negative.
Hence, the equation |x| = 11 has two solutions: x = 11 and x = -11.
To graph this equation, we plot these two points on the number line:
-11 ------------ 0 ------------ 11
So the graph would have a filled-in circle at -11 and another filled-in circle at 11, representing the two solutions.
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