Question

How do you solve `-\frac { 1} { 3} ( x + 5) \geq - \frac { 4} { 9} ( x - 2)`?

Answer 1

x ∈ [23;+∞>

Explanation:

`-1/3(x+5)>=-4/9(x-2)`

multiplying by 27 because 3*9=27

then
`-9(x+5)>=-12(x-2)`
distributive property

`-9x-45>=-12x+24`

transposing terms
`12x-9x>=24+45`

`3x>=69`

finally
`x>=23`

then x ∈ [23;+∞>

Answer 2

`x>= 23`

Explanation:

`"to eliminate the fractions multiply both sides of the "`
`"inequation by the "color(blue)"lowest common multiple"`
`"of 3 and 9"`

`"the lowest common multiple of 3 and 9 is 9"`

`cancel(9)^3xx-1/cancel(3)^1(x+5)>=cancel(9)^1xx-4/cancel(9)^1(x-2)`

`rArr-3(x+5)>=-4(x-2)`

`"distributing brackets gives"`

`-3x-15>=-4x+8`

`"add "4x" to both sides"`

`-3x+4x-15>=cancel(-4x)cancel(+4x)+8`

`rArrx-15>=8`

`"add 15 to both sides"`

`xcancel(-15)cancel(+15)>=8+15`

`rArrx>=23" is the solution"`