Question

Solve the inequality. 1/3+x+2/9


`\geqslant`
5/6
A)x

`\geqslant`
1 7/18
B)x

`\geqslant`
5/18
C)x

`\geqslant`
17/18
D)x

`\leqslant`
17/18

​

Answer 1

`$(1)/(3)+x+(2)/(9)\ge (5)/(6)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge (5)/(18)\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.27777\dots \\ \:\mathrm{Interval\:Notation:}&\:[(5)/(18),\:\infty \:)\end{bmatrix}$`

Explanation:

`$(1)/(3)+x+(2)/(9)\ge (5)/(6)$`

`\gray{\mathrm{Group\:like\:terms}}`

`$x+(1)/(3)+(2)/(9)\ge (5)/(6)$`

`\black{\mathrm{Least\:Common\:Multiplier\:of\:}3,\:9:\quad 9}`

`\black{\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}}`

`$(3)/(9)+(2)/(9)\ge (5)/(6)$`

`$\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)}$`

`$(3+2)/(9)\ge (5)/(6)$`

`\gray{\mathrm{Add\:the\:numbers:}\:3+2=5}`

`$x+(5)/(9)\ge (5)/(6)$`

`$\gray{\mathrm{Subtract\:}(5)/(9)\mathrm{\:from\:both\:sides}}$`

`$x+(5)/(9)-(5)/(9)\ge (5)/(6)-(5)/(9)$`

`\gray{\mathrm{Simplify}}`

`$x\ge (5)/(18)$`