Solving Two-Step Equations: Division by a Number

Key Concepts

• This lesson focuses on solving two-step equations where a number is divided into the variable, rather than multiplied.
• The example given is ( \frac{Y}{6} - 3 = -11 ).

Process for Solving

Step 1: Convert to Fractions

• Visualize all terms as fractions:
  • ( -11 ) becomes ( \frac{-11}{1} )
  • ( -3 ) becomes ( \frac{-3}{1} )

Step 2: Eliminate Fractions

• Multiply every term by the common denominator to eliminate fractions:
  • Common denominator is 6
  • Use distributive property to distribute ( \frac{6}{1} ) to both sides of the equation

Step 3: Simplification

• Perform multiplication:
  • Left side becomes ( 6Y - 18 )
  • Right side becomes ( -66 )
• Simplify:
  • ( \frac{6Y}{6} = Y )
  • ( -18 ) remains
  • Equation becomes ( Y - 18 = -66 )

Step 4: Solve the Simplified Equation

• Add 18 to both sides to isolate ( Y ):
  • ( Y = -66 + 18 )
  • Result: ( Y = -48 )

Verification

• Substitute ( Y = -48 ) back into the original equation to check:
  • ( \frac{-48}{6} = -8 )
  • ( -8 - 3 = -11 )
• ( -11 = -11 ) confirms the solution is correct.

Tips for Solving Equations

• Remember to perform the same operations on both sides of the equation to maintain balance.
• Always check your solution by substituting back into the original equation.
• Keep track of negative and positive signs, especially when determining the sign of the final answer.