Question

How do you solve `2x\sqrt{5}-\frac{1}{4}>3x+\frac{2}{3}`?

Answer 1

`x > 11/(24sqrt(5)-36)`

Explanation:

Given
`color(white)("XXX")2xsqrt(5)-1/4 > 3x+2/3`

Since we can always add or subtract the same amounts from both sides of an inequality
`color(white)("XXX")2sqrt(5)x-3x > 2/3+1/4`

Simplifying
`color(white)("XXX")(2sqrt(5)-3)x > 8/12+3/12`

and since `(2sqrt(5)-3) > 0` we can divided both sides by this without changing the direction of the inequality
`color(white)("XXX")x > (11/12)/(2sqrt(5)-3)`

`color(white)("XXX")x > 11/(24sqrt(5)-36)`

If desired, you could use a calculator to approximate the expression on the right side of the inequality above.