Question

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

Answer 1

x =
`(17)/(4)` (17/4 = 4.25)

or x =
`-(31)/(4)` (-31/4 = -7.75)

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 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=
`(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 =
`-(31)/(4)`

so, we know that

x =
`(17)/(4)` (17/4 = 4.25)

or x =
`-(31)/(4)` (-31/4 = -7.75)

hope this helps!!

Answer 2

x = -31/4 or x = 17/4

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