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

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-04-11T16:29:30+02:00

ANSWER

[tex]x \leqslant \frac{1}{2} \: or \: x \geqslant \frac{3}{4} [/tex]

EXPLANATION

The 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]

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-03-28T11:17:23+02:00

The solution set of the inequality is (c) [tex]x \le \frac 12[/tex] or [tex]x \ge \frac 34[/tex]

The inequality is given as:

[tex](4x-3)(2x-1) \ge 0[/tex]

Split the above inequality

[tex](4x-3) \ge 0[/tex] or [tex](2x-1) \ge 0[/tex]

Remove the bracket

[tex]4x-3 \ge 0[/tex] or [tex]2x-1 \ge 0[/tex]

Rewrite as:

[tex]4x \ge 3[/tex] or [tex]2x \ge 1[/tex]

Solve for x

[tex]x \ge \frac 34[/tex] or [tex]x \ge \frac 12[/tex]

Rewrite as:

[tex]x \le \frac 12[/tex] or [tex]x \ge \frac 34[/tex]

Hence, the solution set of the inequality is (c) [tex]x \le \frac 12[/tex] or [tex]x \ge \frac 34[/tex]