Solve any linear equation in one variable — fractions, decimals, parentheses, variables on both sides.
ax + b = cx + d
One Solution: When you move all x terms to one side, the coefficient of x is non-zero. You can divide to isolate x and get a single numeric answer. This is the most common case.
No Solution: When all x terms cancel and the remaining constants are not equal (e.g. 3 = 7). The equation is a contradiction — no value of x can ever make it true.
Infinite Solutions: When all x terms and all constants cancel, leaving 0 = 0 (always true). Every real number satisfies the equation — the two sides are identical expressions.
Substitute x back into the original equation
After solving, plug your answer back into the original equation and simplify both sides. If both sides equal the same number, your answer is correct.
Example: For 3x + 7 = 2x − 5 with x = −12:
LHS: 3(−12) + 7 = −36 + 7 = −29
RHS: 2(−12) − 5 = −24 − 5 = −29
−29 = −29 ✓
One-on-one Algebra tutoring builds the confidence to tackle any equation — we work through your actual homework and tests so the strategies become second nature.