Linear Equation Solver

How to use

1. Enter one equation like “2x+3=7” (exactly one “=”).
2. Press “Calculate”.
3. See the tidy-up, transposition, and division steps, plus a check line.

Examples

• 2x+3=7 → x=2
• 3x-5=x+1 → x=3
• -x/2+1=4 → x=-6

When to use it (grade level)

Linear equations are taught in earnest in the first year of middle school. You use a letter such as x to stand for an unknown number and practice finding its value. This tool suits lesson preview and review, checking home study, and confirming your work before a test.

A linear equation is an equality like 2x+3=7 that contains x to the first power only. Finding the value of x that makes the equality true is called “solving” the equation. For example, the solution of 2x+3=7 is x=2.

How to work it out yourself

First, gather the x-terms on the left and the number-only terms on the right. For 2x+3=7, move +3 to the right to get 2x=7-3=4. Then divide both sides by the coefficient of x (the number in front of x). Dividing 2x=4 by 2 gives x=2.

It works the same when x appears on both sides. For 3x-5=x+1, move the right x to the left and the left -5 to the right: 3x-x=1+5, so 2x=6, and dividing by 2 gives x=3. When the answer does not divide evenly, keep it as a fraction such as x=3/2.

What transposition really is — from the properties of equality (a balance scale)

An equation (two expressions joined by “=”) is easiest to picture as a balanced scale. A scale stays balanced if you add the same weight to both pans, or remove the same weight from both. That is the property of equality: adding, subtracting, multiplying, or dividing (by a non-zero number) both sides by the same amount keeps the equation true.

This property gives us “transposition”. Take x+3=8. Subtracting 3 from both sides keeps it equal: x+3-3=8-3, so x=5. The +3 on the left looks as if it moved to the right with its sign flipped to -3. That is transposition. Conversely, for x-4=1, add 4 to both sides to get x=5; the -4 becomes +4 as it moves right.

Handling the coefficient uses the same idea. For 2x=8, dividing both sides by 2 keeps it equal, so x=4. Dividing both pans of the scale by the same number does not upset the balance. Transposition is not magic — it is just a short way of writing these properties of equality, which makes calculations more reliable.

Common mistakes

Three slip-ups are common. First, forgetting to flip the sign when transposing — moving +3 must make it -3. Second, forgetting to divide: writing 2x=4 as x=4 instead of dividing by 2 to get x=2. Third, operating on only part of the equation; the property of equality requires doing the same thing to both sides, never adding or dividing on just one side.

When the answer is a fraction, forcing it into a decimal can introduce rounding errors. This tool keeps fractions exact and shows results such as x=3/2.

Related topics and tools

When a linear equation gives a fractional answer, you need fraction arithmetic. Practicing common denominators and simplifying with the fraction calculator helps. Word problems about proportions often turn into linear equations, so pairing this with the percentage tool builds your ability to set up equations too. Try each problem yourself first, then use this tool to check the steps.

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