Question

How do you solve `49- [ 3+ 10y - 4( y + 2) ] = - 5( 3y - 6) - [ 5( y - 1) - 9y + 21]`?

Answer 1

Arrange the equation

Explanation:

`49 - 3 -10y + 4y + 8 = -15y + 30 -5y +5 +9y -21`

after getting rid of parantheses:

`49 - 3 +8 - 30 -5 +21 = -15y -5y +9y +10y -4y`

Now combine numbers on one side and y terms on the other:

`40 = -24y + 19 y`

`40 = -5y`

`y=-40/5 = -8`

Your answer is `y=-8`

Answer 2

`y=-8`

Explanation:

Given: `49- [ 3+ 10y - 4( y + 2) ] = - 5( 3y - 6) - [ 5( y - 1) - 9y + 21]`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider "-[3+10y-4(y+2)]`

Multiply inside the square brackets by `-1`

`-3-10y+4(y+2)`

`-3-10y+4y+8`

`-3+8 -10y+4y`

`color(white)("dd")+5 color(white)("dddd")-6y`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider " - 5( 3y - 6))`

Multiply everything inside the brackets by `-5`

`-15y+30`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider "- [ 5( y - 1) - 9y + 21])`

Multiply inside the square brackets by `-1`

`-5(y-1)+9y-21`

`-5y+5+9y-21`

`+5-21-5y+9y`

`color(white)("d")-16color(white)("dddd")+4y`
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`color(blue)("Putting it all back together")`

`49+5-6y=-15y+30-16+4y`

`54-6y=-11y+14`

`11y-6y=14-54`

`5y=-40`

`y=-8`