Scientific Notation Calculator

Equation Solver

Isolate any variable in a linear equation, follow each algebraic step, and verify the answer by substitution back into the original equation.

Solve one-variable linear equationsStep-by-step algebraic breakdownVerify answers by substitution

Equation Solver

Solve one-variable equations with exact linear/quadratic handling and numerical roots for broader equations.

Ready

Supports one variable, implicit multiplication, powers, roots, logs, and trig functions in radians.

Step by Step

    Result Summary

    Solutions
    x = 4
    Equation
    2x + 3 = 11

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    Converter

    Notation converter

    Convert between scientific notation, decimal notation, engineering notation, and E notation.

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    Equation Solver

    An equation solver finds the value of an unknown variable that makes both sides of an equation equal. Linear equations, where the variable appears only to the first power, are the most common type in algebra, physics, and everyday problem-solving. The calculator accepts equations with one variable, simplifies both sides, isolates the variable through inverse operations, and returns the solution with each algebraic step explained.

    What Is a Linear Equation?

    A linear equation is a mathematical statement that two expressions are equal and where the variable appears only to the first power. The equation 3x + 5 = 20 states that 3x + 5 and 20 are equal for some specific value of x. Solving it means finding that value: subtracting 5 from both sides gives 3x = 15, and dividing by 3 gives x = 5. Substituting back confirms 3(5) + 5 = 20. Linear equations have exactly one solution, no solution, or infinitely many solutions depending on their structure. You isolate the variable by applying the correct inverse operations at each step.

    How to Use the Equation Solver

    Type the equation into the input field using x (or another variable) on either or both sides. The solver accepts standard arithmetic operators, fractions written as numerator/denominator, and parentheses for grouped terms. Valid inputs include: 3x + 5 = 20, 2(x − 3) = 4x + 1, and x/2 + 3 = 7.

    Click Solve. The results panel displays the value of the variable and a numbered step-by-step solution showing each inverse operation applied. A substitution check confirms that the found value makes both sides of the original equation equal.

    Worked Examples

    Examples: 3x + 5 = 20 → x = 5; 2(x − 3) = 4x + 1 → x = −3.5; x/4 − 2 = 3 → x = 20; 5x = 3x + 14 → x = 7; and 0.5x + 1.2 = 3.7 → x = 5.

    Common Equation Types

    Common tasks include solving for a variable in distance to rate to time formulas (d = r × t), isolating variables in Ohm's law (V = IR), solving percent equations, and working through two-step equations in algebra coursework.

    Linear Equation Solving Methods

    These tables list the main steps and properties used to isolate a variable in one-variable linear equations.

    One-step equations: addition and subtraction

    To isolate a variable in a one-step additive equation, apply the inverse operation to both sides.

    EquationInverse operationStep resultSolution
    x + 7 = 12Subtract 7 from both sidesx = 12 − 7x = 5
    x − 4 = 9Add 4 to both sidesx = 9 + 4x = 13

    One-step equations: multiplication and division

    To isolate a variable in a one-step multiplicative equation, apply the inverse by dividing or multiplying both sides by the same non-zero value.

    EquationInverse operationStep resultSolution
    4x = 28Divide both sides by 4x = 28 / 4x = 7
    x/3 = 5Multiply both sides by 3x = 5 × 3x = 15

    Two-step equations

    Two-step equations need two inverse operations. Undo the addition or subtraction first, then undo the multiplication or division.

    EquationStep 1Step 2Solution
    3x + 5 = 20Subtract 5: 3x = 15Divide by 3x = 5
    2x − 7 = 9Add 7: 2x = 16Divide by 2x = 8

    Variable on both sides

    Collect all variable terms on one side and all constants on the other by adding or subtracting the smaller variable term from both sides.

    EquationCollect variable termsCollect constantsSolution
    5x = 3x + 145x − 3x = 14 → 2x = 14Divide by 2x = 7
    6x − 2 = 4x + 82x = 10Divide by 2x = 5

    Equations with parentheses

    Use the distributive property to expand parentheses first, then collect like terms and isolate the variable.

    EquationDistributeCollect termsSolution
    2(x + 3) = 102x + 6 = 102x = 4x = 2
    3(2x − 1) = 156x − 3 = 156x = 18x = 3

    Equations with fractions

    Clear fractions by multiplying both sides by the least common denominator (LCD) of all fractional terms before solving.

    EquationLCDCleared equationSolution
    x/2 + 1 = 4LCD = 2x + 2 = 8x = 6
    x/3 − x/6 = 2LCD = 62x − x = 12x = 12

    Verifying solutions by substitution

    Check your answer by substituting the value back into the original equation. If both sides are equal, the solution is verified.

    EquationSolutionSubstitution checkVerified
    3x + 5 = 20x = 53(5) + 5 = 20 ✓Yes
    2x − 7 = 9x = 82(8) − 7 = 9 ✓Yes

    Process

    Calculation workflow

    Enter equation
    Distribute and simplify
    Isolate the variable
    Verify by substitution

    The solver parses the equation, distributes any parentheses, collects like terms, applies inverse operations step by step to isolate the variable, and confirms the result by substituting the solution back into the original equation.

    Input formats

    Supported formats

    Input styleExample
    Two-step equation3x + 5 = 20
    Variable on both sides5x = 3x + 14
    With parentheses2(x − 3) = 4x + 1
    With fractionsx/2 + 3 = 7

    Reference

    Common scientific constants

    Back to calculator
    Constant nameSymbolNotation valueUnit
    Speed of lightc2.99792458 x 10^8m/s
    Gravitational constantG6.67430 x 10^-11N m^2/kg^2
    Avogadro constantNA6.02214076 x 10^23mol^-1

    Questions

    Calculator FAQ

    What is a linear equation?

    A linear equation is one where the variable appears only to the first power and is not inside a radical, exponent, or denominator that contains the variable. Its graph is a straight line and it has at most one solution.

    How do I solve an equation?

    Isolate the variable by applying inverse operations to both sides. Undo addition and subtraction first, then undo multiplication and division. Every operation must be applied equally to both sides.

    What does it mean to isolate a variable?

    Isolating a variable means rearranging the equation so the variable stands alone on one side with a coefficient of 1. The other side then equals the solution.

    What is the distributive property?

    The distributive property states that a(b + c) = ab + ac. When an equation has parentheses, expand them using this property before combining like terms.

    How do I solve 3x + 5 = 20?

    Subtract 5 from both sides to get 3x = 15. Then divide both sides by 3 to get x = 5. Check: 3(5) + 5 = 20 confirms the solution.

    How do I solve an equation with fractions?

    Multiply both sides by the least common denominator of all fractions in the equation. This clears the fractions and leaves a simpler equation to solve.

    What does 'no solution' mean in a linear equation?

    A linear equation has no solution when the variable cancels out and the remaining constants are unequal. For example, 2x + 3 = 2x + 7 simplifies to 3 = 7, which is never true.

    What does 'infinitely many solutions' mean?

    An equation has infinitely many solutions when the variable cancels and the remaining statement is always true. For example, 3x + 6 = 3(x + 2) simplifies to 6 = 6, which is true for any value of x.

    How do I check a solution?

    Substitute the value back into the original equation and evaluate both sides. If both sides produce the same number, the solution is correct.

    What are like terms?

    Like terms contain the same variable raised to the same power. In 4x + 3x − 2, the terms 4x and 3x are like terms and combine to give 7x − 2.

    What is a two-step equation?

    A two-step equation requires exactly two inverse operations to isolate the variable. For example, 2x + 4 = 10 is solved by subtracting 4 (step 1) and then dividing by 2 (step 2).

    How do I solve for x when it appears on both sides?

    Move all x terms to one side by adding or subtracting the smaller x term from both sides. Then solve the resulting one-variable equation normally.

    Can I solve equations with decimal coefficients?

    Yes. Treat decimal coefficients the same as integers. You can optionally multiply both sides by a power of 10 to clear the decimals before solving, or work directly with the decimal values.

    What operations can I apply to both sides of an equation?

    You can add, subtract, multiply, or divide any non-zero value to both sides while preserving equality. Dividing by zero is not allowed.

    What is the difference between an equation and an expression?

    An expression is a combination of numbers and operators with no equals sign, such as 3x + 5. An equation asserts two expressions are equal, such as 3x + 5 = 20, and can be solved for the variable.

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