What is the solution set to the inequality (4x-3)(2x-1) greater than or equal to 0?

Accepted Solution

ANSWER[tex]x \leqslant \frac{1}{2} \: or \: x \geqslant \frac{3}{4} [/tex]EXPLANATIONThe given inequality is:[tex](4x - 3)(2x - 1) \geqslant 0[/tex]We solve the corresponding quadratic equation to obtain,[tex](4x - 3)(2x - 1) = 0[/tex]This implies that;[tex]x = \frac{3}{4} \: or \: x = \frac{1}{2} [/tex]We use the number line to solve the inequality as shown in the attachment.[tex]x \leqslant \frac{1}{2} \: or \: x \geqslant \frac{3}{4} [/tex]