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Linear inequalities
An inequality gives a range of answers rather than one. Solve it almost exactly like an equation.
Symbols and number lines
< less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to.
On a number line, an open circle means the value is not included (<, >). A filled circle means it is included (≤, ≥).
On a number line, an open circle means the value is not included (<, >). A filled circle means it is included (≤, ≥).
Solving
Use the same balancing steps as an equation.
3x + 4 < 19 → 3x < 15 → x < 5
Warning: if you multiply or divide by a negative number, flip the inequality sign.
3x + 4 < 19 → 3x < 15 → x < 5
Warning: if you multiply or divide by a negative number, flip the inequality sign.
Integer solutions
−2 < n ≤ 3, where n is an integer: n = −1, 0, 1, 2, 3.
The −2 is not included (strict), the 3 is included.
The −2 is not included (strict), the 3 is included.
Solve 5 − 2x ≥ 11.
- Subtract 5: −2x ≥ 6
- Divide by −2 and flip the sign: x ≤ −3
Answer: x ≤ −3
Solve inequalities like equations, but flip the sign when multiplying or dividing by a negative. Open circles for < and >, filled for ≤ and ≥.
Check you have got it
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