Variable on Both Sides Challenge
Solve equations with variables on both sides using systematic algebraic steps to collect like terms.
Current Equation
Solve for x:
3x + 5 = 2x + 11
Left coefficient: 3
Left constant: 5
Right coefficient: 2
Right constant: 11
Solution: x = 6
Solution Steps:
Complete each step to solve the equation:
1. Move variables to the left side:
3x + 5 - x = 2x +
11 - x
Strategy: Collect all variable terms on one side and constants on the other
Variables on Both Sides Guide
General Form: ax + b = cx + d
- • a, c are coefficients of x on left and right sides
- • b, d are constant terms on left and right sides
- • Goal: Collect all x terms on one side, constants on the other
Solution Strategy:
- • Step 1: Subtract the smaller coefficient from both sides
- • Step 2: Subtract constants to isolate the variable term
- • Step 3: Divide by the remaining coefficient if needed
- • Step 4: Check by substituting back into original equation
Example: 3x + 5 = 2x + 11
- • Step 1: 3x + 5 - 2x = 2x + 11 - 2x → x + 5 = 11
- • Step 2: x + 5 - 5 = 11 - 5 → x = 6
- • Check: 3(6) + 5 = 18 + 5 = 23, and 2(6) + 11 = 12 + 11 = 23 ✓
Pro Tips:
- • Always subtract the smaller coefficient to avoid negative coefficients
- • Keep track of signs when moving terms
- • Check your answer by substituting into both sides
- • If you get a negative coefficient, consider moving terms differently
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Progress
Complete Step 1 to begin
Step Progress:
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2
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4
Move variables to one side first
Variable Collection Techniques
Key Strategy:
- • Collect all variable terms on one side
- • Collect all constant terms on the other side
- • Subtract the smaller coefficient first
- • Apply inverse operations systematically
- • Maintain equation balance throughout
Common Mistakes:
- • Forgetting to subtract from both sides
- • Sign errors when moving terms
- • Not collecting like terms properly
- • Mixing up which terms to move
- • Arithmetic errors in final calculation
Pro Tips:
- • Choose the side with the larger coefficient
- • Work step-by-step, don't rush
- • Double-check your arithmetic
- • Always verify by substitution
- • Use the visual to check reasonableness