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Solve for X Calculator

To solve for x in 2x + 3 = 11, subtract 3 from both sides to get 2x = 8, then divide by 2.

Use ^ for powers and * or nothing for multiplication: 2x, 2*x and 2(x) all work. One variable, any single letter.

Solutionx = 4

The equation
2x + 3 = 11
Everything to one side
2x - 8 = 0
Divide by 2
x = 4
Check Exactly zero, computed in fractions rather than decimals, so this is a proof rather than a round-off that looks close.
putting x = 4 into 2x - 8 gives 0
  • Linear and quadratic equations are solved exactly. Higher degrees start with the rational root theorem, which finds every rational root. What is left is solved exactly where a formula applies and numerically where none does, complex roots included, and every root is checked by substitution.
  • Polynomials in one variable. Trigonometry, logarithms, roots of expressions and calculus are outside what this does, and it names them rather than failing obscurely.

How the Algebra Calculator works

Solving for x means getting x alone on one side of the equals sign, and the only rule is to do the same thing to both sides. Each step undoes one operation, in the reverse of the order the equation applied them.

In 2x + 3 = 11, x was doubled and then had 3 added. Undo the addition first: subtract 3 from both sides to get 2x = 8. Then undo the doubling: divide both sides by 2 to get x = 4. Put 4 back in to check it: 2(4) + 3 = 11.

The answer is not always a whole number. 3x = 2 gives x = 2/3, and the solver keeps it as a fraction because no decimal writes it exactly.

Two outcomes are not a single number. If x cancels out and what is left is true, as in 2x + 2 = 2(x + 1), every value of x works. If what is left is false, as in x + 1 = x + 2, no value does. The solver says which.

Algebra Calculator FAQ

How do I solve for x?

Expand any brackets, collect like terms, move everything to one side so the equation reads something = 0, then divide by the coefficient of x. For 3(x + 4) - 2x = 5x - 8 that gives -4x + 20 = 0, so x = 5. Always substitute your answer back in to check it.

Why does this give fractions instead of decimals?

Because the fraction is the exact answer and the decimal is a rounding of it. 3x = 1 solves to exactly 1/3, and 0.3333333333 is a different number. Working in floating point makes x/3 + 1/6 = 1/2 solve to 0.9999999999999998: nearly right, which is worse than visibly wrong.

What does it mean when there is no solution?

The variable canceled out and left a false statement. 2(x + 1) = 2x + 3 simplifies to 2 = 3, which no value of x can fix. The opposite case is an identity, like 2(x + 1) = 2x + 2, where the variable cancels and leaves something true. Then every value works.

Can it solve cubic equations?

Yes. It first uses the rational root theorem: any rational root p/q has p dividing the constant term and q dividing the leading coefficient, which gives a finite list to test. Rational roots come out exactly. A factor with no rational roots is then solved numerically, complex roots included, and each root is checked by substitution.

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