ALGEBRA

Solve a linear equation ax + b = c for x. Enter the coefficient, constant, and right-hand side.

a (coefficient of x)

b (constant)

c (right side)

Solution (x)

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Value of x.

Usage Tip

Whatever you do to one side, do to the other: subtract b from both sides, then divide both by a.

THE MATH

ax + b = c → x = (c − b) ÷ a
Undo the constant, then undo the coefficient

A linear equation in one variable has a single solution when the coefficient of x is non-zero.
Solving means isolating x by reversing the operations.

Enter a, b, and c for the equation ax + b = c.
If a is zero there is either no solution or infinitely many.
The check column substitutes the answer back in.

Practical Notes

A linear equation of the form ax + b = c has one unknown, and it is solved by getting x alone. Subtract b from both sides, then divide by a, so x equals c minus b, divided by a. For example, 3x + 4 = 19 gives x = 5.

The coefficient a cannot be zero, because then x disappears from the equation. If a is zero, the equation either has no solution or is true for every value of x, depending on whether b equals c. You can always check an answer by putting it back into the original equation. Linear equations model costs with a fixed fee, distances at a constant speed, and any situation with a steady rate.

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