Inequality Basics
Solve:
7 + x < 15
x < 8
Solve: −3x > 21
x < −7
Graph x > 2.
Open circle at 2
Which symbol means “less than or equal to
≤
When do you flip the inequality sign?
When multiplying or dividing both sides by a negative number.
Graph x ≤ −5. Which direction do you shade?
Shade left
Inequality: 4x − 3 > 9.
What is the solution?
x > 3
Solve:
5 − 2x < −9
x > 7
Graph the solution to:
4x + 8 ≥ 0
x ≥ −2 (closed circle, shade right)
True or false: −2 > −5
True
Solve and flip if needed:
−8 ≥ 4 − 2x
x ≥ 6
Which inequality has a closed circle:< , > , ≤ , or ≥ ?
≤ and ≥
Write an inequality to represent:
“A number decreased by 6 is at least 10.”
x − 6 ≥ 10
A student solved:
−5x ≤ 20 → x ≤ −4
What mistake did they make?
They forgot to flip the sign. Correct solution: x ≥ −4
What is the graph for all real numbers less than −3?
Open circle at −3, shade left