Linear Equation Solver Challenge
Solve equations with linear expressions on one side and numbers on the other using algebraic steps.
Current Equation
Solve for x:
3x + 5 = 17
Coefficient: 3
Constant: 5
Right side: 17
Solution: x = 4
Solution Steps:
Complete each step to solve the equation:
1. Subtract the constant from both sides:
3x + 5 - = 17 -
Tip: Apply the same operation to both sides to keep the equation balanced
Linear Equation Solution Guide
General Form: ax + b = c
- • a is the coefficient of x
- • b is the constant term on the left side
- • c is the number on the right side
- • Goal: Isolate x to find its value
Solution Strategy:
- • Step 1: Subtract b from both sides → ax = c - b
- • Step 2: Divide both sides by a → x = (c - b)/a
- • Step 3: Simplify the fraction if needed
- • Step 4: Check by substituting back into original equation
Example: 3x + 5 = 17
- • Step 1: 3x + 5 - 5 = 17 - 5 → 3x = 12
- • Step 2: 3x ÷ 3 = 12 ÷ 3 → x = 4
- • Check: 3(4) + 5 = 12 + 5 = 17 ✓
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Equation Solving Techniques
Key Principles:
- • Whatever you do to one side, do to the other
- • Work systematically through each step
- • Use inverse operations to isolate x
- • Addition and subtraction are inverses
- • Multiplication and division are inverses
Common Mistakes:
- • Forgetting to apply operations to both sides
- • Mixing up addition and subtraction
- • Incorrect order of operations
- • Not checking the final answer
- • Calculation errors in arithmetic
Pro Tips:
- • Always check your answer by substitution
- • Work step-by-step, don't skip steps
- • Keep track of positive and negative signs
- • Simplify fractions when possible
- • Use the visual representation to verify