Q: When do I flip the inequality sign?

Whenever you multiply or divide both sides by a negative number. -3x > 6 becomes x < -2. Adding or subtracting never flips the sign.

Q: What is the difference between "and" and "or" in the answer?

"And" means x has to satisfy both, so you keep only the overlap of the two solution sets. "Or" means either one works, so you keep everything in either set. "And" can produce no solution; "or" can produce all real numbers.

Q: How do I write the answer in interval notation?

Use a round bracket for an endpoint that is not included (strict ) and a square bracket for one that is (≤ or ≥). Infinity always gets a round bracket. Join two separate pieces with the union symbol ∪.

Question 1

What is a compound inequality?

Accepted Answer

Two inequalities joined by "and" or "or". An "and" compound inequality like -3 < 2x + 1 ≤ 7 is often written as one double inequality. An "or" compound inequality like x < -1 or x ≥ 3 stays as two pieces.

Question 2

When do I flip the inequality sign?

Accepted Answer

Whenever you multiply or divide both sides by a negative number. -3x > 6 becomes x < -2. Adding or subtracting never flips the sign.

Question 3

What is the difference between "and" and "or" in the answer?

Accepted Answer

"And" means x has to satisfy both, so you keep only the overlap of the two solution sets. "Or" means either one works, so you keep everything in either set. "And" can produce no solution; "or" can produce all real numbers.

Question 4

How do I write the answer in interval notation?

Accepted Answer

Use a round bracket for an endpoint that is not included (strict < or >) and a square bracket for one that is (≤ or ≥). Infinity always gets a round bracket. Join two separate pieces with the union symbol ∪.

Question 5

How do I graph the solution on a number line?

Accepted Answer

Open circle for < or >, closed (filled) circle for ≤ or ≥, then shade the part of the line where the solution lives. The calculator draws this for you under the answer.