Answer: [tex]x<\frac{2}{5}[/tex]
Step-by-step explanation:
[tex](2x+3)(4x-1)<8x^2+1[/tex]
Begin by multiplying parentheses.
[tex](2x*4x)+(2x*-1)+(3*4x)+(3*-1)<8x^2+1[/tex]
[tex](8x^2)+(-2x)+(12x)+(-3)<8x^2+1[/tex]
[tex]8x^2-2x+12x-3<8x^2+1[/tex]
Subtract [tex]8x^2[/tex]
[tex]8x^2-2x+12x-3+(-8x^2)<8x^2+1+ (-8x^2)[/tex]
[tex]-2x+12x-3<1[/tex]
Add 3
[tex]-2x+12x-3+3<1+3[/tex]
[tex]-2x+12x<4[/tex]
Combine like terms;
[tex]10x<4[/tex]
Divide by 10
[tex]x<\frac{4}{10}[/tex]
Simplify;
[tex]x<\frac{2}{5}[/tex]
