How do you graph and solve #abs(x+1)+x+1<-1#?

Answer 1

The inequation has not solutions.

#abs(x+1)+x+1<-1# or
#abs(x+1)+x+10#
Now, for #x ne -1#
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Answer 2

Invalid inequality. No solution at all.

If so, 2x+1 must be #< -1#, since #|x+1| = x + 1# for #x > = -1.#.

Moreover, for this to occur,

Since #x < -3/2 < -1#, this case is eliminated.
Thus, for x #< = -1.#, #|x+1| = -(x + 1)#. If this is the case,
x+1) + #-(x+1)=0 > -1#.

Thus, this case is also disqualified.

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Answer 3

To graph and solve the inequality ( |x + 1| + x + 1 < -1 ), you first solve the equation ( |x + 1| + x + 1 = -1 ) to find the boundary points. Then, you graph the solution on a number line and determine the solution set based on the inequality.

  1. Solve the equation ( |x + 1| + x + 1 = -1 ): ( |x + 1| + x + 1 = -1 ) ( |x + 1| = -1 - x - 1 ) ( |x + 1| = -x - 2 )

    Since the absolute value of a number cannot be negative, there are no solutions for this equation.

  2. Graph the inequality on a number line: Since there are no solutions to the equation, there are no boundary points to graph. Therefore, the graph of the inequality ( |x + 1| + x + 1 < -1 ) is an empty set on the number line.

  3. Solve the inequality: Since there are no boundary points to include in the solution, the solution set for the inequality ( |x + 1| + x + 1 < -1 ) is an empty set, represented as ( \emptyset ). Therefore, there are no real solutions to the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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