Read the equation before solving

In ax + b = c, a is the multiplier on x, b is the constant already attached to the left side, and c is the target value. Solving means undoing those operations in reverse order.

Isolate x in two moves

Subtract b from both sides.
Divide by a when a is not zero.
Check whether a zero coefficient creates every-solution or no-solution behavior.

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General solution path

Subtract the constant before dividing by the x coefficient.

Original form

a x + b = c

Subtract b

a x = c - b

Solve for x

x = \frac{c - b}{a}, a \neq 0

Every solution case

If a = 0 and b = c, every x is a solution

No solution case

If a = 0 and b \neq c, there is no solution

Check the result

Substitute the expression for x back into the original equation.

Substitution check

Check: a (\frac{c - b}{a}) + b = c

FAQ

Why do I subtract b before dividing by a?

Because b is added after ax; subtracting it first restores the isolated product ax.

What happens when a is zero?

Then x has no multiplier in the equation. If b = c, every value of x works. If b != c, no value of x works.

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