Enter a complete equation and follow the same operation on both sides until x is isolated. Restrictions and special cases remain visible beside the answer.
Result
Remove the constant, clear the denominator, and divide by the coefficient without changing the equality.
x=10
Conditions
x is a real variable.
Both sides are defined for every value considered.
The input is a linear equation after valid simplification.
Steps
Remove the outside constant Subtract 1 from both sides.43(x−2)=6
Clear the denominator Multiply both sides by 4.3(x−2)=24
Undo the multiplication Divide both sides by 3.x−2=8
Isolate x Add 2 to both sides.x=10
✓
Independent check
Substitution gives 3(10-2)/4+1=6+1=7, which matches the right side.
Scope
What this solve-for-x covers
To solve for x, simplify each side, move variable terms to one side, move constants to the other, and divide by the remaining coefficient. An identity has infinitely many solutions, while a contradiction has no solution.
One-step equations
Undo a single addition, subtraction, multiplication, or division.
Examples: x+8=13, 5x=35
Multi-step equations
Distribute and combine like terms before isolating x.
Examples: 4(x+1)=3x+9, 2(x-3)+5=11
Fractional equations
Clear constant denominators with a common nonzero multiplier, then solve the equivalent equation.
Examples: x/5-2=3, (x-1)/3=(x+5)/6
Variables on both sides
Collect x-terms to reveal one solution, an identity, or a contradiction.
Examples: 5x-4=2x+11, 5x+2=5x+2, 4x-1=4x+3
How to use it
Enter enough information for one clear task
1
Write both sides completely
Use an equals sign and parentheses around every grouped numerator or distributed expression.
2
Simplify before isolating
Distribute and combine like terms on each side so the coefficient of x is clear.
3
Keep the equation balanced
Every addition, subtraction, multiplication, or division used to isolate x must be applied to both sides.
4
Substitute into the original
A valid solution makes the original left and right sides defined and equal, not merely the final transformed line.
Worked inputs
Examples to try
Use these examples to recognize the method, compare equivalent forms, and check your own work.
Addition and division
Subtract 5 and divide by 2.
2x+5=17
Expected result
x=6
Negative coefficient
Subtract 7, then divide by negative 3.
7−3x=−8
Expected result
x=5
Variable on both sides
Distribute, subtract 3x, and subtract 4.
4(x+1)=3x+9
Expected result
x=5
Fraction coefficient
Add 2 and multiply by 5.
5x−2=3
Expected result
x=25
Fractions on both sides
Multiply by 6 and solve the resulting linear equation.
3x−1=6x+5
Expected result
x=7
Identity
Subtracting matching sides leaves a true statement.
5x+2=5x+2
Expected result
x∈R
Contradiction
Subtracting 4x leaves the false statement -1=3.
4x−1=4x+3
Expected result
∅
Complete example
Clear two denominators without losing balance
The least common denominator is 6. Multiplying the entire equation by 6 removes both denominators in one valid step.
32(x+6)−2x=5
1
Multiply every term by 6
Apply the same nonzero multiplier to both sides.
4(x+6)−3x=30
2
Distribute and combine
Expand 4(x+6), then combine the x-terms.
4x+24−3x=30
3
Isolate x
The left side is x+24, so subtract 24 from both sides.
x=6
x=6
Verification: The original left side becomes (2/3)(12)-6/2=8-3=5, equal to the right side.
Avoidable errors
Common mistakes and how to fix them
Changing only one side
Problem: Subtract 4 from the left side but leave the right side unchanged.
Why it matters: That creates a different equation rather than an equivalent one.
Better approach: Write the same operation on both sides before simplifying.
Clearing only one denominator
Problem: Multiply one fractional term by the common denominator and ignore the other terms.
Why it matters: A multiplier applied to an equation must multiply every term on both sides.
Better approach: Use parentheses around each side, then distribute the common denominator to every term.
Treating every linear equation as one-solution
Problem: Report x=0 after the x-terms cancel.
Why it matters: Cancellation can leave a true identity or a false contradiction.
Better approach: Classify a true statement as all real solutions and a false statement as no solution.
Dividing by the wrong sign
Problem: From -3x=-15, report x=-5.
Why it matters: A negative divided by a negative is positive.
Better approach: Write x=(-15)/(-3)=5 and verify it in the original equation.
Trust the result for the right reasons
Checks, assumptions, and limits
How results are checked
The isolated value is substituted into the original equation.
Identity and contradiction cases are classified from the final truth value.
Each denominator is checked before and after clearing fractions.
When to stop and revise the input
The equation must be linear after valid simplification for this focused calculator.
Variable denominators require explicit domain restrictions and may produce excluded candidates.
An expression without an equals sign does not define a solve-for-x task.
Common questions
Solve for x FAQ
What does it mean to isolate x?
It means writing an equivalent equation with x alone on one side. Each operation used to reach that form must preserve the same solution set.
Can a linear equation have no solution?
Yes. If the variable terms cancel and leave a false statement, such as -1=3, no value of x satisfies the original equation.
When does a linear equation have infinitely many solutions?
If simplification produces a true identity, such as 2=2, both sides represented the same expression. Every real x allowed by the original domain is then a solution.
Why should I clear fractions first?
Multiplying by a common nonzero denominator often makes the equation easier to read. It is optional, and any original denominator restrictions still apply.
How do I check a value of x?
Replace x with the value in the original equation and simplify both sides independently. The check succeeds only when both sides are defined and equal.
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