Back to: Algebra 1
An inequality is a mathematical relationship between two expressions and is represented using one of the following symbols:
≤: “less than or equal to,”
<: “less than,”
>: “greater than,”
≥: “greater than or equal to.”
Note: Pay close attention to phrases such as “at most” (≤) or “at least” (≥).
Example: The sum of 8y and 3y is greater than 66.
In symbols, 11y > 66
y > 6 Therefore y cannot be 6, it must be greater than 6.
Example: The sum of a number and 5 is at most 23.
In symbols, n + 5 ≤ 23 “At most” means less than or equal to.
n ≤ 19
Example: The weight of the truck w, plus its load of two thousand pounds must be at least four thousand pounds.
In symbol, w + 2000 ≥ 4000 “At least” means greater than or equal to.
w ≥ 2000
Example: Solve the inequality,
27 < x – 3
+3 +3
———————
30 < x
Example: Solve the equation,
– 10 + x > 30
+10 +10
——————-
x > 40