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Deffense [45]
2 years ago
13

|4x + 7| − 4 = 20 Can anyone help me with this

Mathematics
2 answers:
Slav-nsk [51]2 years ago
7 0

Answer:

x = \frac{17}{4}    (17/4 = 4.25)

or x =  -\frac{31}{4}  (-31/4 = -7.75)

Step-by-step explanation:

| | is notation for absolute value

absolute value - the distance that a number is from 0

> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |

if we have | x | = 20, we could really have (without the | | ) two versions of x

either | x | = 20  ; or | -x | = 20  {because a negative x inside of the | | has the same value as positive x}

we set this up as two equations:

x = 20        or         -x = 20

                                ^ {multiply by -1}

x = 20  or   x = -20

now, let's plug our understanding into the equation

|4x + 7| - 4 = 20

first, we should simplify our equation to:

|4x + 7| - 4 = 20

           + 4   + 4

 |4x + 7|   =   24

now, let's separate this absolute value equation into two separate equations:

4x + 7 = 24:

      - 7    - 7  {subtract 7 from both sides to isolate x}

4x = 17

÷4  ÷4        {divide both sides by 4 to get 1x}

x= \frac{17}{4}

or,

4x + 7 = -24:

      - 7    -7   {subtract 7 from both sides to isolate x}

4x     =    -31

÷4           ÷4   {divide both sides by 4 to get 1x}

 x = -\frac{31}{4}

so, we know that

x = \frac{17}{4}    (17/4 = 4.25)

or x =  -\frac{31}{4}  (-31/4 = -7.75)

hope this helps!!

Reil [10]2 years ago
6 0

Answer:

x = -31/4  or x = 17/4

Step-by-step explanation:

|4x + 7| − 4 = 20

⇔ |4x + 7| − 4 + 4 = 20 + 4

⇔ |4x + 7| = 24

⇔ 4x + 7 = 24  or 4x + 7 = -24

⇔ 4x = 24 - 7 or 4x = -24 - 7

⇔ 4x = 17 or 4x = -31

⇔ x = 17/4 or x = -31/4

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