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Algebra solver solve for x: an algebra x solver with steps

Type an equation and this algebra solver solves for x, an algebra x solver that works one line at a time: what was done to both sides, why it is allowed, and a final check that puts the answer back into the original equation. It works for equations with x on both sides, brackets, quadratics, and formulas with other letters in them.

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    Algebra x solver: what happens on each line

    To solve for x you undo what has been done to x, in reverse order, and do the same thing to both sides each time. Move the x terms together, move the plain numbers to the other side, then divide by the number in front of x. This algebra x solver writes that order out. If there are brackets, they are expanded first. If x appears twice, the x terms are collected on one side.

    The four examples below go from an equation with x on both sides, to one with brackets, to a quadratic with two answers, to a formula where the answer is written with another letter. In every case the last line is a check you can repeat yourself.

    One answer, two answers, or an expression

    A linear equation in x usually has one answer. A quadratic can have two, and both should be checked. A formula such as 5x − 2y = 12 cannot give a number, because y is unknown too, so solving for x means writing x in terms of y: x = (2y + 12)/5. The solver says which of these cases applies. For an equation with x in a denominator or under a root, it also lists the values x cannot take.

    How to use it

    1. Type the equation with an equals sign. Use ^ for powers and * or brackets for products, for example 2(x - 3) + 5 = 4x - 9.
    2. Say which letter to solve for when there is more than one, for example "solve for x".
    3. Read each line: the move on the left, the reason underneath.
    4. Look at the check line. It substitutes the answer into the original equation and compares both sides.

    Algebra solver solve for x: worked examples with steps

    Each example is the solver's own output for the equation shown. We also solved every one by hand, and the answers match. Use the link under an example to run it on the board above.

    1. Solve 3x + 7 = 2x - 5 for x

    1. Subtract 2x from both sides3x - 2x + 7 = -5Subtract 2x from both sides of the equation to collect all variable terms on the left.
    2. Simplify the left sidex + 7 = -5Combine the like terms 3x and -2x to get x.
    3. Subtract 7 from both sidesx = -5 - 7Subtract 7 from both sides to isolate the variable x.
    4. Simplify the right sidex = -12Combine the constant terms -5 and -7 to find the value of x.

    Answer: x = -12

    Check: Substitute x = -12 back into the original equation: Left-hand side is 3(-12) + 7 = -36 + 7 = -29. Right-hand side is 2(-12) - 5 = -24 - 5 = -29. Both sides are equal, confirming the solution is correct.

    Solvecam board showing the step-by-step solution of: Solve 3x + 7 = 2x - 5 for x

    Open this example on the board above →

    2. Solve 2(x - 3) + 5 = 4x - 9 for x

    1. Expand the parentheses2x - 6 + 5 = 4x - 9Distribute 2 to each term inside the parentheses: 2 * x = 2x and 2 * (-3) = -6.
    2. Combine like terms on the left side2x - 1 = 4x - 9Combine the constant terms -6 and +5 to get -1.
    3. Subtract 2x from both sides-1 = 2x - 9Subtract 2x from both sides to group the variable terms on one side.
    4. Add 9 to both sides8 = 2xAdd 9 to both sides to isolate the term containing x.
    5. Divide both sides by 2x = 4Divide both sides by the coefficient 2 to solve for x.

    Answer: x = 4

    Check: Substitute x = 4 back into the original equation: Left side: 2(4 - 3) + 5 = 2(1) + 5 = 7. Right side: 4(4) - 9 = 16 - 9 = 7. Both sides are equal, confirming the solution is correct.

    Open this example on the board above →

    3. Solve x^2 + 2x - 15 = 0 for x

    1. Find two numbers that multiply to -15 and add to 25 * (-3) = -15 and 5 + (-3) = 2Look for factors of the constant term (-15) whose sum equals the coefficient of the middle term (2).
    2. Factor the quadratic expression(x + 5)(x - 3) = 0Rewrite the quadratic equation as a product of two linear binomials.
    3. Apply the zero-product propertyx + 5 = 0 or x - 3 = 0If the product of two factors is zero, at least one of the factors must be zero.
    4. Solve each linear equation for xx = -5 or x = 3Isolate x by subtracting 5 from both sides of the first equation and adding 3 to both sides of the second.

    Answer: x = -5, 3

    Check: Substitute each value into the original equation: for x = 3, (3)^2 + 2(3) - 15 = 9 + 6 - 15 = 0; for x = -5, (-5)^2 + 2(-5) - 15 = 25 - 10 - 15 = 0. Both solutions satisfy the equation.

    Solvecam board showing the step-by-step solution of: Solve x^2 + 2x - 15 = 0 for x

    Open this example on the board above →

    4. Solve 5x - 2y = 12 for x

    1. Add 2y to both sides5x = 2y + 12Use the addition property of equality to isolate the x-term on the left side of the equation.
    2. Divide both sides by 5x = (2y + 12) / 5Use the division property of equality to solve for x by dividing both sides by its coefficient, 5.

    Answer: x = (2y + 12)/5

    Check: Substitute x = (2y + 12)/5 into the original equation: 5 * ((2y + 12)/5) - 2y = (2y + 12) - 2y = 12, which matches the right-hand side.

    Solvecam board showing the step-by-step solution of: Solve 5x - 2y = 12 for x

    Open this example on the board above →

    Common slips when solving for x

    • Changing a sign when moving a term to the other side. Subtracting 2x from both sides is safer to write than "moving" it.
    • Multiplying a bracket by only its first term.
    • Stopping at 8 = 2x instead of dividing to get x = 4.
    • Giving only one answer to a quadratic.

    Which kind of equation is it

    If x appears only to the first power, the equation is linear. If it has x² it is quadratic, and you can often factor it. If x is in a denominator, use the algebra fraction solver. If x is inside a square root, use the radical math solver. For an inequality, use the inequalities solver.

    Use it to learn the method. Try the problem on paper first, then compare your lines with the steps. The first line where you differ is the thing to practise. Solutions are written by an AI model and can contain mistakes, so keep the check line in the habit.

    FAQ

    How do I solve for x in an equation?

    Collect the x terms on one side and the numbers on the other, then divide by the number in front of x. Do the same operation to both sides each time, and check the answer in the original equation.

    Can it solve for x when there are other letters?

    Yes. The answer is then an expression, as in x = (2y + 12)/5. Say which letter to solve for if it is not obvious.

    What if there are two answers?

    A quadratic can have two. The solver gives both and checks each one in the original equation.

    Can I type the equation or must I upload it?

    Either. Type it in the box, or take a photo of a printed or neatly handwritten equation.

    Is it free?

    Yes. You get 3 full solutions a day with no account. The examples on this page do not count against that.

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