Question

How do you solve `4x+2[4-2(x+2)]=2x-4`?

Answer 1

x =10 Start with the inner parenthesis and work outward. Then solve for x by combining like terms and working backwards.

Explanation:

One way to remember how to solve for an unknown is to think

If you lose something in PE you are a SAD M (an)

Translation do Parenthesis and Exponents first then SA do subtracting and addition which ever comes first. The D M multiplication and division which ever comes first.

In the this problem do the inner parenthesis first

#-2( x + 2 ) = -2x + 4

Next do the the second parenthesis which now looks like

`2 ( 4 -2x + 4) = 8 - 4x + 8`

The equation now looks like

4x + 8 - 4x + 8 = 2x -4.

use the communicative property to group like terms

4x - 4x + 8 + 8 = 2x -4 this gives

  16  = 2x -4

add + 4 to both sides as + 4 is the opposite of -4

16 + 4 = 2x -4 + 4 = 20 = 2x

divide both sides by 2 because dividing is the opposite of multiplying

`20/2 = 2xx x/2`

10 = x

Answer 2

`x = 2`

Explanation:

`4x + 2[4-2color(magenta)((x+2)] = 2x -4`

Usually we would start with the bracket, but they are unlike terms - so use the distributive law to remove the brackets.
Try to keep the equal signs under each other

`" "4x + 2[4color(red)(-2)(x+2)]"" = 2x -4`
`" "4x + 2[4color(red)(-2x-4)]" "= 2x -4 " simplify"`
`" "4x + 2[color(red)(-2x)] " "= 2x -4" multiply out the bracket"`
`" "4x color(red)(-4x) " "= 2x color(blue)(-4)`
`" "color(blue)(4)= 2x`
`" "2= x`