Determine the interval of values of x if |3x+5|<10

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

l 3x + 5 l < 10

That means:

3x + 5 < 10       or   -(3x+5) <10

3x + 5 < 10        or  3x + 5 > -10

==> -10 < 3x + 5 < 10

Now subtract 5:

==> -15 < 3x < 5

Divide by 3:

==> -5 < x < 5/3

Then x belongs to the interval (-5, 5/3)

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

-10<3x+5<10

We'll solve first:

-10<3x+5

We'll add -5 both sides:

-15<3x

We'll divide by 3 both sides:

-5<x

Now, we'll solve:

3x+5<10

We'll subtract 5 both sides, in order to isolate x:

3x<5

We'll divide by 3 both sides:

x<5/3

So, the range of values of x is:

-5<x<5/3

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the interval values for |3x+5| < 10

Solution:

If3x+5 > 0, the 3x+5 <10 by definition

3x< 10-5 =5

x < 5/3.

If 3x+5 < 0, then 3x+5 > -10 by definition.

3x > -10+5 = -5

x > -5/3.

So combining the two possibilities,

-5/3 <x < 5/3 Or x belongs to the open interval (-5/3 , 5/3)

 

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