Solving & Graphing Inequalities (Grade 6)
An inequality compares two amounts that aren't necessarily equal, using <, >, ≤, or ≥.
Understanding solving & graphing inequalities
"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). One difference comes later: multiplying or dividing both sides by a negative number flips the sign, so 5 > 3 becomes −5 < −3. The problems here only add, subtract, or use positive numbers. 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).
Open circle: 5 itself is not included. The arrow covers every number greater than 5.
A common mistake, and the fix
Treating the answer as one number, or including the boundary when it isn’t included.
x + 2 > 7 gives x > 5: every number greater than 5 works, such as 5.5, 6 or 100, but 5 itself doesn’t, because 5 + 2 = 7 is not greater than 7. On a number line that is an open circle at 5.
Try a few
x − 3 < 4
add 3 to both sides.
Is x ≥ 6 satisfied by x = 6?
≥ includes the boundary.
2x ≤ 10
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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