Algebra

Inequalities

Easy

core

The solution set of the inequality $3x+4y<12$ is

An open half-plane not containing the origin

An open half plane containing the origin

The whole xy-plane not containing the line $3x+4y=12$

A closed half-plane containing the origin

✅ Correct Option: 2

The line $3x+4y=12$ splits the plane into two half-planes.

Testing the origin: $3(0)+4(0)=0<12$ , which satisfies the inequality.

Since the inequality is strict, the boundary line is excluded, so the solution is an open half-plane containing the origin.

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The solution set for the inequality $|5x-3| \le \dfrac{1}{5}$ is:

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The solution to the inequality $-12 < \frac{2x-1}{3} < 12$ is

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The solution set of the inequation $4x + 3y > 5$ is

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Which of the following shaded regions represents the solution to the inequation $|x|+|y| \leq 1$ ?

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If $\frac{1}{|x| - 3} \leq \frac{1}{2}$ , then value of $x$ :

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Solution of the inequality $\frac{2x+3}{4x-5} \geq 0$ is

The solution set of the inequality 3x+4y<123x+4y<123x+4y<12 is