Math: Algebra

Isolate the variable: subtract 5 (3x = 15), then divide by 3 (x = 5). Undo addition/subtraction first, then multiplication/division.

Distribute: 2x - 8 = 10. Add 8: 2x = 18. Divide by 2: x = 9.

Collect variables on one side: 5x - 2x = 9 + 3, so 3x = 12, x = 4.

Subtract 2: x/3 = 4. Multiply both sides by 3: x = 12. (Or clear fractions first by multiplying every term by 3.)

When simplifying yields a false numeric statement (variables cancel, leaving e.g. 0 = 5). The lines never meet because coefficients match but constants differ.

When the variable cancels and you get a true identity (e.g. 0 = 0 or 3 = 3); both sides are equivalent expressions, true for all x.