Practice Algebraic Constraint in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A mathematical condition expressed as an equation or inequality that restricts which values the variables are allowed to take.

x2+y2=1 constrains (x,y) to lie on a circle — not all points in the plane are allowed.

Showing a random 20 of 50 problems.

Example 1

easy
What constraint does x place on x (real numbers)?

Example 2

medium
Why can the constraint x>0 and x<0 never be satisfied together?

Example 3

hard
For what real k does x2+kx+9=0 have two distinct real roots?

Example 4

medium
The constraint 2x+3=3+2x restricts x to what set?

Example 5

medium
For x+1x−2, state all domain constraints.

Example 6

easy
What domain constraint does 1x2−9 impose?

Example 7

medium
How many integer solutions (x,y) satisfy x+y=6 with x,y≥1?

Example 8

easy
What constraint on x makes log⁡(x) defined (real, principal branch)?

Example 9

challenge
For x,y>0 with xy=4, find the minimum of x+y.

Example 10

medium
Maximize 4x+3y subject to x+y≤4, x≥0, y≥0.

Example 11

easy
What domain constraint does x−3 impose (over the reals)?

Example 12

medium
If x+y=10 and x,y>0, what is the maximum of xy?

Example 13

hard
x+1=x−1. Solve and check.

Example 14

challenge
Find the minimum of x2+y2 subject to x+2y=5.

Example 15

medium
What values does 1x−3 constrain x to avoid?

Example 16

hard
xx−2≥0. Solve.

Example 17

medium
A rectangle has perimeter 20 with length ℓ and width w. Write the constraint and the implicit ones.

Example 18

easy
Which describes a constraint: x+3 or x+3=7?

Example 19

challenge
Find all integer points satisfying x+y=4 with x,y≥0.

Example 20

medium
Solve x2=9 subject to the constraint x>0.
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