|-10+e^x|<9
Answered question
2022-04-21
|-10+e^x|<9
Answer & Explanation
nick1337
Expert2022-05-08Added 777 answers
Write as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
In the piece where is non-negative, remove the absolute value.
To find the interval for the second piece, find where the inside of the absolute value is negative.
Solve the inequality.
Add to both sides of the inequality.
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
In the piece where is negative, remove the absolute value and multiply by .
Write as a piecewise.
Simplify .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality...
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
Find the intersection of and .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality.
Divide each term in by and simplify.
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
The natural logarithm of is .
Find the intersection of and .
Find the union of the solutions.
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
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