Question

How do I solve this?

Answer 1

x >
`(83)/(15)`

Explanation:

Given

`(x-5)/(2)` +
`(2)/(5)` >
`(2)/(3)`

Multiply through by 30 ( the LCM of 2, 5 and 3 ) to clear the fractions

15(x - 5) + 12 > 20 ← distribute and simplify left side

15x - 75 + 12 > 20

15x - 63 > 20 ( add 63 to both sides )

15x > 83 ( divide both sides by 15 )

x >
`(83)/(15)`

Answer 2

`x>(83)/(15)`

Explanation:

STEP 1: Simplify
`(x-5)/(2) +(2)/(5)>(2)/(3)`

`(5x-21)/(10)>(2)/(3)`

STEP 2: Multiply both sides of the equation by
`10`.

`(5x-21)/(10)>(2)/(3)*(10)`

STEP 3: Remove parentheses.

`(5x-21)/(10)>(2)/(3)*(10)`

STEP 4: Multiply
`(2)/(3)*(10)`

`(5x-21)/(10)>(20)/(3)`

STEP 5: Move all terms not containing
`x` to the right side of the inequality.

`5x>(83)/(3)`

STEP 6: Divide each term by
`5` and simplify.

`x>(83)/(15)`

STEP 7: The result can be shown in multiple forms.

Inequality Form:

`x>(83)/(15)`

Interval Notation:

`((83)/(15)`,∞
`)`