Subtract 16 from both sides: - Coaching Toolbox

Understanding the Context

When we say “subtract 16 from both sides,” we’re referring to a key algebraic property: performing the same operation on both sides of an equation preserves equality. This rule ensures that the equation remains balanced.

Let’s begin with a simple example:

Step 1: Start with the equation
x – 16 = 5

Step 2: To isolate x, subtract 16 from both sides:
x – 16 – 16 = 5 – 16
This simplifies to:
x – 32 = –11

Key Insights

Step 3: Now x is alone on the left, and the equation reads:
x = –11 + 32 = 21

Why Subtract 16?

Subtracting 16 eliminates the constant term on the left side, bringing you closer to solving for the unknown variable. This technique is essential when manipulating equations in algebra, physics, economics, and everyday problem-solving.

More Examples: Subtracting 16 in Different Contexts

Final Thoughts

• Word Problem: “A tank initially holds 16 gallons of water. After draining, it contains 5 gallons. How much water was removed?”
  Model this as: Initial – removed = Remaining → x – 16 = 5 → solve: x = 21

• Finance: If your account balance dropped by $16 and now shows $5, how much was withdrawn? Again: Balance – 16 = 5 → solve for initial balance.

• Geometry & Physics: These operations help balance equations involving distance, velocity, or charge when unknowns are involved.

Key Takeaways

• Subtracting a number from both sides maintains equation balance.
  
• It’s a core step in solving linear equations.
  
• Useful across scientific, financial, and everyday calculations.
  
• Always apply the same operation to both sides to preserve equality.