# Solve |x+5|+13>15?

Relevance
• 15 = 15/1 = 15*5/5 x = 75

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• |x + 5| + 13 > 15

Solutions:

x > -3

x < -7

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• Step 1: Add -13 to both sides.

|x+5|+13+−13>15+−13

|x+5|>2

Step 2: Solve Absolute Value.

|x+5|>2

We know either x+5>2 or x+5<−2

x+5>2(Possibility 1)

x+5−5>2−5(Subtract 5 from both sides)

x>−3

x+5<−2(Possibility 2)

x+5−5<−2−5(Subtract 5 from both sides)

x<−7

x>−3 or x<−7

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• |x+5|+13>15

=>

|x+5|>2

=>

x+5>2

or

x+5<-2

=>

x>-3 or x<-7

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Original inequality:

|x + 5| + 13 > 15

Subtract 13 from both sides:

|x + 5| > 2

You are dealing with an absolute value, so there are two cases to consider:

x+5 is negative or x+5 is positive.

CASE 1 - Positive

x + 5 > 2

Subtract 5 from both sides:

x > -3

CASE 2 - Negative

-(x + 5) > 2

Multiply both sides by -1, remember when multiplying by a negative, switch the direction of the inequality symbol:

x + 5 < -2

Subtract 5 from both sides:

x < -7

x < -7 or x > -3

Or in interval notation:

(-∞, -7) ∪ (-3, ∞)

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• |x+5|+13>15

|x + 5| > 2

x + 5 > 2 or x + 5 < -2

x > -3 or x < -7

in interval notation: (-∞, -7) U (-3, +∞)

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• |x + 5| + 13 > 15

Solutions:

x > -3

x < -7

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• First suppose x >= -5; in that case,

x + 5 + 13 > 15 => x > -3.

Next, suppose x < -5; in that case

-x - 5 + 13 > 15 => -x > 7, so x < -7.

The solution set is

(-infinity,-7) U (-3,+infinity)

• Yes but on my online system it only says my answer is 50% correct when i enter either of those figures?

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• |x + 5| + 13 > 15

|x + 5| > 2

x + 5 > 2 or x + 5 < -2

x > -3 or x < -7

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• Anonymous
9 months ago

That’s not even a complete equation.

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