Question

(2x+3)(4x-1)<8x^(2)+1

Answer 1

Answer:
`x<(2)/(5)`

Explanation:

`(2x+3)(4x-1)<8x^2+1`

Begin by multiplying parentheses.

`(2x*4x)+(2x*-1)+(3*4x)+(3*-1)<8x^2+1`

`(8x^2)+(-2x)+(12x)+(-3)<8x^2+1`

`8x^2-2x+12x-3<8x^2+1`

Subtract
`8x^2`

`8x^2-2x+12x-3+(-8x^2)<8x^2+1+ (-8x^2)`

`-2x+12x-3<1`

Add 3

`-2x+12x-3+3<1+3`

`-2x+12x<4`

Combine like terms;

`10x<4`

Divide by 10

`x<(4)/(10)`

Simplify;

`x<(2)/(5)`