Mrs.D Math · 8th Grade

ALL
CLEAR

Inequalities with Rational Numbers · Operations
⚖️ Inequalities
🧰 Fractions
💧 Decimals
⚖️ Clear the fraction: × LCM
💧 Clear the decimal: × 10
🔄 ÷ by a negative? FLIP!
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Solving Inequalities with Fractions

Multiply every term by the LCM of the denominators to clear the fractions — then solve like an equation.

1
Find the LCM of all denominators.
x/2 + 3 < x/4 + 5  →  LCM = 4
2
Multiply every term by the LCM.
2x + 12 < x + 20
3
Collect x on one side and solve.
x < 8

Solving Inequalities with Decimals

Multiply every term by a power of 10 (10, 100, ...) to clear the decimals.

1
Count decimal places — tenths need ×10, hundredths need ×100.
0.4x + 1.2 ≤ 0.2x + 2  →  ×10
2
Multiply every term.
4x + 12 ≤ 2x + 20
3
Solve.
2x ≤ 8  →  x ≤ 4

⚠️ The Golden Rule & How to Play

🔄
FLIP the inequality symbol whenever you multiply or divide both sides by a negative number.
−2x < 6  →  x > −3
🧰
Fractions — clear denominators with the LCM, then solve. Choose from 4 answers.
💧
Decimals — clear decimals with a power of 10, then solve.
🧮
Calculator — tap the gold button in the corner any time. Try it in your head first, then verify!
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FRACTIONS
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