Free Algebra MCQs with Answers

• A. 14
• B. 15
• C. 20
• D. 16

Explanation: Let's denote the unknown number as xThe average of 4 and x being smaller than 10 can be expressed as:4+x/2= 10Files sale with genuine Chce…

• A. two disjoint regions
• B. four disjoint regions
• C. left and right half planes
• D. four planes

Explanation: The graph of a linear equation of the form + = ax+by=c represents a straight line on the plane.

• A. left and right half planes
• B. upper and lower half planes
• C. four planes
• D. None

Explanation: A nonvertical line divides the plane into upper and lower half planes. This is because any nonvertical line can be represented by an…

• A. left and right half planes
• B. upper and lower half planes
• C. four planes
• D. None

Explanation: When a nonvertical line divides the plane, it separates the plane into two distinct regions or half planes.

• A. solid line
• B. dashes
• C. dots
• D. None

Explanation: When the inequality involves the symbols > or <, it represents strict inequalities.

• A. solid line
• B. dashes
• C. dots
• D. None

Explanation: When the inequality involves the symbols ≥ or ≤, it represents nonstrict inequalities.

• A. boundary line
• B. right half plane
• C. left half plane
• D. None

Explanation: The set of ordered pairs \((x, y)\) such that \(ax + by < c\) forms a region known as a halfplane.

• A. open half planes
• B. closed half planes
• C. open and closed half planes
• D. None

Explanation: The graph of the inequalities \(ax + by \leq c\) and \(ax + by \geq c\) represent closed half planes.

• A. stationary point
• B. test point
• C. corner point
• D. None

Explanation: A point of a solution region where two of its boundary lines intersect is called a corner point.

• A. problem constraints
• B. feasible region
• C. feasible solution
• D. None

Explanation: The system of linear inequalities involved in a problem are called problem constraints.

• A. negative constraints
• B. positive constraints
• C. nonnegative constraints
• D. None

Explanation: Decision variables are typically subject to nonnegative constraints. This means that the values of decision variables must be greater than…

• A. decision variables
• B. problem constraints
• C. feasible solution
• D. None

Explanation: Each point of the feasible region is called a feasible solution. A feasible solution is a point within the feasible region that satisfies…

• A. objective function
• B. explicit function
• C. feasible function
• D. optimal solution

Explanation: A function which is to be maximized or minimized in optimization problems is called the objective function.

• A. infinite
• B. finite
• C. two
• D. three

Explanation: In some theoretical scenarios or special cases, the feasible solution region may be unbounded or extend infinitely in some directions.

• A. simple solution
• B. feasible solution
• C. optimal solution
• D. None

Explanation: The feasible solution that maximizes or minimizes the objective function is called the optimal solution.

• A. closed half plane
• B. open half plane
• C. line only
• D. full plane

Explanation: The graph of the inequality \(3x + 2y > 3\) represents an open half plane.

• A. Circle
• B. Open half plane
• C. Parabola
• D. Plane

Explanation: The solution set of the inequality \(ax + by < c\) is an open half plane.

• A. an equation
• B. an inequality
• C. both a and b
• D. None

Explanation: A statement that contains at least one of the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or…

• A. variables
• B. constraints
• C. solution
• D. None

Explanation: Nonnegative constraints often refer to constraints on variables in optimization problems, requiring them to be nonnegative.

• A. Ellipse
• B. Circle
• C. Region
• D. None

Explanation: The graph of a linear inequality with two variables represents a region in the coordinate plane.