What are inverse operations?
Inverse operations are pairs that cancel each other: addition and subtraction, multiplication and division, squaring and square roots. Solving for x is mostly a matter of applying the right inverse to both sides.
The both-sides part matters. An equation is a balance, and whatever you do to one side you must do to the other, or the two sides stop being equal.
Every step of the solver is one of these inverse moves applied to both sides, or a cleanup step like distributing or combining like terms. If you can name which inverse a step uses, you understand that step.
| If x has been… | Undo it by… |
|---|---|
| added to (x + 7) | subtracting 7 |
| subtracted from (x − 7) | adding 7 |
| multiplied (3x) | dividing by 3 |
| divided (x/4) | multiplying by 4 |
| squared (x²) | taking ± the square root |
How do you solve 3x − 7 = 11?
Add 7 to both sides, then divide both sides by 3. The answer is x = 6.
The 7 goes first because it's the last thing that happened to x. Start with x, multiply by 3, subtract 7. Unwinding runs backwards, so the subtraction comes off before the multiplication.
What does a math equation solver do?
A math equation solver finds the value of the unknown that makes both sides of an equation equal. You give it 3x − 7 = 11 and it returns x = 6, along with each step it took and a check that 3(6) − 7 comes out to 11.
This one handles linear, quadratic and polynomial equations up to degree 6. It also solves equations with fractions or x in a denominator, square root equations, and exponent equations like 3^(x + 1) = 27. For two or more unknowns, the system of equations calculator is the right tool.
Can you solve for a variable other than x?
Yes. This equation solver treats any single letter as the unknown, which makes it a solve for variable calculator as much as a solve for x one. You can type 4t + 1 = 9 and get t = 2, or 2y + 1 = 7 and get y = 3. The steps are identical to solving for x.
Pasted instructions work too. "Solve for b: 2b − 5 = 9" returns b = 7. The equation needs to have one unknown letter, though. A formula like d = rt with three letters is outside what it does, and for two unknowns with two equations you'd use the system of equations calculator.
Using a different letter can feel strange at first, but nothing about the method depends on the letter. In physics and finance you'll solve for t (time), r (rate) or P (principal) far more often than x, so it's good practice.
What if x is on both sides of the equation?
Move all the x terms to one side first, by adding or subtracting, and then solve as usual. It doesn't matter which side you collect them on, though picking the side with the bigger x coefficient avoids negatives.
Sometimes the x terms cancel completely. If what's left is false, like 0 = −5, there's no solution. If it's always true, like 0 = 0, every number works. The linear equation calculator page covers both cases.
How do you solve for x with fractions?
You can clear the fractions by multiplying both sides by the lowest common denominator, or you can work with them as they are. Both give the same answer.
Take x/3 + 1/2 = 5/6. Multiply every term by 6 and you get 2x + 3 = 5, so 2x = 2 and x = 1. The solver keeps the fractions instead: it subtracts 1/2 to get (1/3)x = 1/3, then divides by 1/3 to reach x = 1.
Type fractions with a slash. Numbers work as fractions or decimals, so 0.5x + 1.2 = 3.7 gives x = 5. Just keep x out of the denominator, because equations like 1/x + 2 = 5 aren't supported.
When does an equation have 2 answers?
When x is squared, there are usually two answers. x² = 9 gives x = −3 or x = 3, because (−3)² and 3² both equal 9.
That's why a square root step is written with ±. Writing only x = 3 is the classic way to lose half the marks. For anything with an x term too, like x² − 5x − 14 = 0, the quadratic equation solver shows factoring and the quadratic formula.
What are common mistakes when solving for x?
The biggest one is doing something to only one side. Subtracting 7 from the left without touching the right breaks the equation.
Another is undoing in the wrong order. In 3x − 7 = 11, dividing by 3 first is allowed, but you must divide every term, giving x − 7/3 = 11/3. Many students divide only the 3x, which gives a wrong answer.
Last, watch signs when you divide by a negative. In −4x + 3 = 19, subtracting 3 leaves −4x = 16, and dividing by −4 gives x = −4, not 4.
How do you solve for x when there are parentheses?
Distribute first, combine like terms, and then solve as normal. Parentheses are the first thing the solver clears, because nothing inside them can move until they're gone.
To check, put −1 into both sides. The left gives 2(−5) + 3 = −7 and the right gives 5(−1) − 2 = −7, so x = −1 is right. Having x end up on the right side is fine: −3 = 3x and 3x = −3 say the same thing.