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How do you solve #abs(x+1)<8#?

Answer 1

Solve two equations one for the positive and one for the negative.
x < 7 and x > -9

The absolute value is the distance form zero. These distance can be either negative or positive. Therefore it is necessary to solve for both the negative and positive values.

so the positive value would be

x + 1 < 8 Subtract 1 from both sides gives

x + 1 -1 < 8 -1 This gives the positive value+

x < 7

The negative value would be

-( x + 1) < 8 This results in

-x - 1 < 8 Add +1 to both sides gives

-x < 9 solve by dividing everything by -1

# -x/-1 < 9/-1# This gives

x > -9

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Answer 2

Genesis Allen

To solve |x + 1| < 8:

Split the inequality into two cases: a) x + 1 < 8 b) -(x + 1) < 8
Solve each case separately: a) x < 7 b) -x - 1 < 8 -x < 9 x > -9
Combine the solutions: -9 < x < 7

So, the solution is -9 < x < 7.

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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.

How do you solve #abs(x+1)&lt;8#?

How do you solve #abs(x+1)<8#?