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

2 Answers
Nov 5, 2017

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;+∞>

Nov 5, 2017

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"