3. Clearing Fractions and Decimals Under Pressure

When the arithmetic gets heavy, convert it to integers immediately. Multiply every term by the LCD (for fractions) or a power of 10 (for decimals).

Example 1:
\[ \frac{2x-1}{3}-\frac{x+2}{4}=\frac{5}{6}. \]
LCD of 3, 4, 6 is 12. Multiply every term by 12:
\[ 4(2x-1)-3(x+2)=10. \]
Distribute:
\[ 8x-4-3x-6=10. \]
Combine:
\[ 5x-10=10,\qquad 5x=20,\qquad x=4. \]

Example 2 - decimals:
\[ 0.15x-0.4=0.05x+1.1. \]
Multiply every term by 100:
\[ 15x-40=5x+110. \]
Collect:
\[ 10x=150,\qquad x=15. \]

Common mistake: multiplying only the fraction terms by the LCD and leaving the lone constant untouched.