Inequality Basics
7 + x < 15
x < 8
Solve: −3x > 21
x < −7
Graph x > 2.
Should the circle be open or closed?
Open circle at 2
What is −7 + 12 ?
5
Solve: 3x + 2 = 14
x = 4
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
Which is greater: −2 or −9?
−2
3x + 30 + x = 10 + 2x + 5x + 2
x = 6
4x − 3 > 9
x > 3
5 − 2x < −9
x > 7
Graph the solution to:4x + 8 ≥ 0
x ≥ −2 (closed circle, shade right)
−6 × −4
24
13(12x − 9) = 12(x + 18)
x = 333 ÷ 144
True or false: −2 > −5
True
Solve: −8 ≥ 4 − 2x
x ≥ 6
Which inequality has a closed circle:
< , > , ≤ , or ≥ ?
Put the numbers in order from least to greatest: −1, −8, 0, −3
−8, −3, −1, 0
9 − 7x = 2x + 45
x = −4
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
True or false: The opposite of −15 is 15
True
A student says the equation
5(x − 3) = 5x − 15
has no solution.
No. Both sides are equal for all x → infinitely many solutions