Solving Equations with Unknowns on Both Sides

Overview

• Equations are like a set of scales that need to stay balanced. Actions on one side must be mirrored on the other.
• The unknown variable is typically represented by letters like x, and can have any value (including negative or decimal).
• Solving involves isolating the variable on one side of the equation.

Solving Equations When Both Unknowns are Positive

• Step 1: Identify which x term to subtract. Choose the one with the smaller coefficient to avoid negative numbers.
• Step 2: Subtract the chosen x term from both sides, maintaining balance.
• Step 3: Simplify the equation to isolate the variable.
• Step 4: Verify the solution by substituting back into the original equation.

Example

1. Start with the equation: (3x + 4 = x + 12).
2. Subtract (x) from both sides: (2x + 4 = 12).
3. Subtract 4 from both sides: (2x = 8).
4. Divide both sides by 2: (x = 4).
5. Verify by substituting (x = 4) back: Both sides equal 16.

Solving Equations When One Unknown is Negative

• Step 1: Add the x term with the negative coefficient to both sides.
• Step 2: Simplify the equation to reduce terms.
• Step 3: Balance the equation by isolating the variable.

Example

1. Start with the equation: (9 - 2x = x + 3).
2. Add (2x) to both sides: (9 = 3x + 3).
3. Subtract 3 from both sides: (6 = 3x).
4. Divide both sides by 3: (x = 2).
5. Verify by substituting (x = 2) back: Both sides equal 5.

Practice and Resources

• Quiz: Test your skills with equations having unknowns on both sides.
• Game - Divided Islands: Interactive exercise available on BBC Bitesize.

Additional Learning

• Explore solving equations with brackets, fractions, and simultaneous equations both algebraically and graphically.

Tips

• Always verify your solution by substituting back into the original equation.
• Practice regularly to improve skill in balancing and solving equations.