Mrs.D Math · 6th Grade

FLIP
SIDE

Multiply & Divide Inequalities · Rational Numbers
> < greater · less
≥ ≤ at least · at most
🔄 Flip when × or ÷ by a negative!
➖3x < 9
🔄 FLIP! → x > −3
📍 then graph it!
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🔄 How Flip Side Works

The Golden Rule of Inequalities

Solve just like an equation — BUT if you multiply or divide both sides by a NEGATIVE number, you must FLIP the inequality sign.

1
−3x < 9 — divide both sides by −3. Negative? FLIP!
−3x < 9  →  x > −3
2
x over −3 < 2 — multiply both sides by −3. Negative? FLIP!
x/(−3) < 2  →  x > −6
3
x on the right? 8 ≤ −2x — divide by −2 and flip: −4 ≥ x. Rewrite with x first:
8 ≤ −2x  →  x ≤ −4
⚠
× or ÷ by a POSITIVE? The sign stays exactly the same. Only negatives flip it!

Graphing the Solution

○
Open circle for > or < — the boundary number is NOT included.
●
Closed circle for ≥ or ≤ — the boundary number IS included.
➞
Shade toward the solutions: > or ≥ shades RIGHT, < or ≤ shades LEFT.
x > −3  →  open circle at −3, arrow to the right

How to Play

🔥
Solve It — Solve the inequality and choose the correct solution from 4 answers. Watch out for the flip trap!
📍
Solve & Graph — Solve it in your head, then BUILD the graph in 3 taps: pick ○ open or ● closed, pick ← or → shading, then tap the boundary number on the number line. Hit CHECK!
🎯
Mixed — Both types together for the ultimate flip challenge!
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