Linear Equation Solver

How it works

Collect the x terms on one side, the numbers on the other, then divide. Fractions and decimals work too. If the x terms cancel, the equation has either no solution or every number as a solution, and the steps show which.

Example

Solve 5x − 3 = 2x + 9.

x = 4

Steps

1. 1
   Start with 5x − 3 = 2x + 9.
2. 2
   Subtract 2x from both sides: 3x − 3 = 9.
3. 3
   Add 3 to both sides: 3x = 12.
4. 4
   Divide both sides by 3: x = 12 ÷ 3 = 4.
5. 5
   Check: left side 17, right side 17.

More examples

Solve 0.5x + 4 = 2x − 5.

x = 6

Steps

1. 1
   Start with 1/2x + 4 = 2x − 5.
2. 2
   Subtract 2x from both sides: −3/2x + 4 = −5.
3. 3
   Subtract 4 from both sides: −3/2x = −9.
4. 4
   Divide both sides by −3/2: x = −9 ÷ (−3/2) = 6.
5. 5
   Check: left side 7, right side 7.

Solve 3x + 7 = 3x − 2.

No solution

Steps

1. 1
   Start with 3x + 7 = 3x − 2.
2. 2
   Subtract 3x from both sides: 7 = −2.
3. 3
   Subtract 7 from both sides: 0 = −9.
4. 4
   That says 0 = −9, which is false, so no number works.

Common mistake

Whatever you do to one side, do to the whole other side. For 3(x + 2) = 12, multiply out or divide both sides by 3 before moving the 2.

Questions

What if one side has no x?

Enter 0 for that side. For 4x − 3 = 9, use c = 0 and d = 9.

How do I enter 3(x + 2) = 12?

Multiply out first: 3x + 6 = 12. Then a = 3, b = 6, c = 0 and d = 12.

What does “every number is a solution” mean?

Both sides are the same expression, like 2x + 4 = 2(x + 2), so any x makes it true.

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