solve the inequalites |4m+8|<12. can you show me the calculations.

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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

Solve:  `|4m+8| < 12`

This means that 4m + 8 is less than 12 units from 0 on a number line, therefore: 

`4m + 8 < 12and 4m + 8 > -12`

Solve each.

`4m + 8 < 12` Subtract 8.

`4m < 4` Divide by 4.

`:. m < 1`

`4m + 8 > -12` Subtract 8.

`4m > -20` Divide by 4.

`:. m > -5`

This makes a final answer of:  `-5 < m < 1`

steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, Quddoos,

For this problem, you would split the inequality up into two inequalities, or a compound inequality.  When the inequality points toward the absolute value like this, the formula is:

|ax+b| < c   becomes

-c < ax+b < c

So, for us, c = 12, a = 4, and b = 8.  So, we have:

-12 < 4x+8 < 12

Then, we solve this for x:

-12 < 4x+8 < 12

-8         -8         -8

-20  <   4x    < 4

   /4        /4        /4

-5  <  x  <  1

So, the answer is -5 < x < 1.

Good luck, quddoos, I hope this assists.

Till Then,

Steve

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The absolute value of (4m + 8) is less than 12.

This gives:

-12 < (4m + 8) < 12

-12 < (4m + 8)

= -20 < 4m

= -5 < m

(4m + 8) < 12

= 4m < 4

= m < 1

Therefore the values of m lie between -5 and 1. The solution set of |4m+8|<12 is (-5, 1)

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

 |4m + 8| < 12

Change the equation to

4m + 8 < 12       and          4m + 8 > -12 now subtract 8 to both sides of both equation

By subtracting , you should get

4m < 4 and 4m > -20 now divide by 4 on both sides of both equation .

By dividing , you should get

m < 1 and m > -5

So your answer is

-5 < m < 1

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`4m+8lt12 `

`4m+8gt-12 `

`4m+8-8lt12-8 `

`4mlt4 `

`(4m)/4lt4/4 `

`mlt1 `

`4m+8gt-12 `

`4m+8-8gt-12-8 `

`4mgt-20 `

`(4m)/4gt(-20)/4`

`mgt-5    `

`-5ltmlt1 `

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