Solving Linear Equations

A linear equation has the form ax + b = c. Solving means isolating x by reversing the operations – subtract b, then divide by a.

Mastery of this process is essential for Chain Reaction and Tangle Trap puzzles, where each step hinges on crisp linear solutions.

Keeping equations balanced is like a scale: any operation applied to one side must be applied to the other. Work systematically – first eliminate constants, then divide out coefficients.

Example: Solve 3x + 5 = 20

1. Subtract 5: 3x = 15
2. Divide by 3: x = 5

Hints and tipa

• Isolate constants first: Move all numbers to the right side (ax = c − b) before dividing by the coefficient.
• Keep one variable per side: Avoid mixing x terms on both sides; combine like terms and then shift them in a single operation.
• Divide carefully: Always write “both sides / a”​ rather than cancelling in your head to avoid sign mistakes.
• Check your solution: Plug your x value back into the original equation to confirm both sides match.
• Beware special cases: If coefficients cancel (0x = 5 or 0x = 0), recognize “no solution” vs. “infinitely many.”