Solving & Graphing Inequalities (Grade 6)
An inequality compares two amounts that aren't necessarily equal, using <, >, ≤, or ≥. "x > 5" means x can be any number greater than 5 — not a single answer but a whole range. You solve inequalities much like equations (do the same to both sides), and you can show the answer on a number line: an open circle for > or < (the boundary is not included), a filled circle for ≥ or ≤ (boundary included).
Understanding solving & graphing inequalities
An inequality compares two amounts that aren't necessarily equal, using <, >, ≤, or ≥. "x > 5" means x can be any number greater than 5 — not a single answer but a whole range. You solve inequalities much like equations (do the same to both sides), and you can show the answer on a number line: an open circle for > or < (the boundary is not included), a filled circle for ≥ or ≤ (boundary included).
Key Idea
An inequality compares two amounts that aren't necessarily equal, using <, >, ≤, or ≥. "x > 5" means x can be any number greater than 5 — not a single answer but a whole range. You solve inequalities much like equations (do the same to both sides), and you can show the answer on a number line: an open circle for > or < (the boundary is not included), a filled circle for ≥ or ≤ (boundary included).
Seeing it in action
Worked example
Solve and describe x + 2 > 7.
Subtract 2 from both sides: x > 5.
So x is any number greater than 5 (open circle at 5, arrow to the right).
The boundary is 5; answers are greater than 5.
Try a few
x − 3 < 4
Is x ≥ 6 satisfied by x = 6?
≥ includes the boundary.
2x ≤ 10
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