68 free MCQs on Linear Inequalities, each with its own worked answer and explanation. Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.
Take the timed Linear Inequalities chapterwise test →68 practice questions on Linear Inequalities, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Linear Inequalities notes.
One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.
Q1.
Which symbol represents a strict inequality?
Q3.
If x > 5, what happens to the inequality if both sides are multiplied by -1?
Q4.
On a number line, how is the boundary point of x > 3 represented?
Q6.
When graphing 2x + 3y <= 12, what kind of boundary line is drawn?
Q7.
To decide which side of a boundary line to shade, what is commonly used?
Q8.
Which of these is a linear inequality in two variables?
Q9.
The solution region of a linear inequality in two variables is called a:
Q11.
If the origin (0,0) satisfies the inequality 4x + 3y <= 12, which side is shaded?
Q12.
The solution of the inequality x + 3 > 5 is:
Q13.
When both sides of an inequality are multiplied or divided by a negative number, the inequality sign:
Q15.
The symbol ≥ means:
Q18.
On a number line, the graph of x > 2 uses an open circle at 2 and shading to the:
Q19.
The solution of the inequality 3x ≥ 9 is:
Q20.
A closed (filled) circle on a number line shows that the endpoint is:
Q22.
Find the solution set of -5 <= 2x - 3 < 7.
Q23.
For the inequality x + y <= 5 with x >= 0, y >= 0, what shape is the feasible region?
Q24.
Solve the system graphically: x + y >= 4 and x + y <= 8 (with x, y >= 0). The feasible region lies:
Q25.
A student scored 62 and 48 in two tests. What minimum score in a third test (out of 100) gives an average of at least 60?
Q26.
Which point satisfies both x - y <= 2 and x + y <= 6 (along with x,y >= 0)?
Q27.
Solve: |2x - 3| < 5 is equivalent to which compound inequality (ignoring absolute value notation)?
Q28.
The graph of 4x + 3y <= 12 in the first quadrant is bounded by the line through which two intercepts?
Q30.
Solve the inequality: (x-2)/3 >= (x-4)/5, for real x.
Q31.
The solution of the inequality −3x > 6 is:
Q33.
The solution of the inequality |x| < 3 is:
Q34.
The solution of the inequality |x| > 2 is:
Q36.
In the coordinate plane, the graph of the inequality x + y ≤ 4 is a:
Q38.
The common solution of x > 1 and x < 5 is:
Q40.
For a system of linear inequalities, the solution region is the ___ of the individual regions:
Q41.
Find all x such that (x-1)(x-2) >= 0 using the sign-rule method for inequalities (not just linear, as an extension exercise).
Q42.
A company makes two products. Constraints from a related LP setup give x >= 0, y >= 0, x + 2y <= 10, and 2x + y <= 10. Which of these is NOT a corner point of the feasible region?
Q43.
For what values of k does the system x + y <= k and x - y <= 2 (with x, y >= 0) have a feasible region that includes the point (3, 1)?
Q44.
Solve for x: (1/(x-2)) > 0, where x is a real number not equal to 2.
Q45.
Two linear inequalities 3x + 4y <= 24 and x + y <= 7 (with x, y >= 0) are graphed together. What are the coordinates of their boundary lines' intersection point?
Q46.
If x is a natural number satisfying 5x - 3 < 3x + 7, how many positive integer solutions are there?
Q47.
A shopkeeper wants the cost price x of an item (in rupees) to satisfy: at least Rs 20 and the selling price (x + 0.25x) to not exceed Rs 100. What is the valid range for x?
Q48.
The solution of the system 2x + y > 4 and x - y < 1 includes which of these points?
Q49.
For the system 3x + 2y <= 18, x + 2y <= 10, x >= 0, y >= 0, what are the coordinates of the corner point where both boundary lines intersect (away from the axes)?
Q50.
Solve the inequality (2x-1)/(x+3) <= 1, for x not equal to -3.
Q51.
The solution of the inequality (x − 1)(x − 3) < 0 is:
Q53.
The solution of the inequality |2x − 1| ≤ 5 is:
Q54.
The number of integer values of x satisfying −2 < x ≤ 3 is:
Q55.
The solution region of the system x ≥ 0 and y ≥ 0 lies entirely in the:
Q56.
The solution of the inequality (x + 2)/(x − 1) > 0 is:
Q57.
If a < b and c < 0, then multiplying the inequality by c gives:
Q58.
The solution of the compound inequality 4 ≤ 2x < 10 is:
Q59.
The greatest integer value of x satisfying 3x + 2 < 14 is:
Q60.
The solution of the inequality x² < 4 is:
Q61.
The solution set of |2x − 1| < 3 is:
Q62.
The solution set of |x − 2| ≥ 5 is:
Q63.
The solution set of (x − 1)/(x − 2) > 0 is:
Q64.
The number of integer points (x, y) with |x| + |y| ≤ 2 is:
Q65.
The solution set of the system 3x − 2 < 2x + 1 and x > 0 is:
Q66.
The solution set of x² − 5x + 6 < 0 is:
Q67.
The solution set of x² − 5x + 6 > 0 is:
Q68.
The solution set of 1/(x − 1) < 2 (x ≠ 1) is:
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