Solve linear algebraic equations of the form ax + b = c with full step-by-step mathematical deduction and solution classification.
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A linear equation in one variable is a first-degree polynomial equation of the canonical form ax + b = c, where a and b are constants and a ≠ 0. It represents a straight line and has exactly one unique real solution.
ax + b = c \implies ax = c - b \implies x = \frac{c - b}{a}Subtract constant b from both sides of the equation, then divide by coefficient a to isolate the variable x.
Scenario: Solve 3x + 7 = 22
Given equation: 3x + 7 = 22
Subtract 7 from both sides: 3x = 22 - 7 = 15
Divide both sides by 3: x = 15 / 3 = 5
A linear equation has an exponent of 1 on all variables. Its graph on a Cartesian coordinate plane is always a straight line.
If a = 0, the variable x vanishes. If the remaining statement is true (e.g. 5 = 5), any real number is a solution; if false (e.g. 5 = 10), no solution exists.
Yes, coefficients can be positive, negative, integers, or floating-point decimal values.
Substitute your calculated x value back into the left side: if the computed result equals the right side (c), the solution is verified.
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