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Linear equations

Isolate the unknown by doing the same thing to both sides.

A linear equation has the unknown to the first power only. Solving it is a sequence of legal moves (add, subtract, multiply or divide both sides by the same thing) chosen to leave the unknown alone. The graph shows the line y = 2x + 3 − 7; the solution is where it crosses the axis.

Umzekelo osebenzelayo · 2x + 3 = 7

Algebra · Linear-Equations

Solve 2x + 3 = 7

2 x + 3 = 7

Inyathelo ngenyathelo

  1. 2 x + 3 = 7

    Start from the equation as given.

  2. 2 x - 4 = 0

    Bring everything to one side and collect like terms so the right-hand side is 0.

  3. 2 x = 4

    Move the constant term to the other side: subtract -4 from both sides.

  4. x = \frac{4}{2}

    Divide both sides by 2, the coefficient of x.

  5. x = 2

    Simplify the fraction.

Bonisa impendulo
x = 2

ngoku Khetha ingxaki, okanye ubhale okanye uzobe yakho. Inyathelo ngalinye, umfanekiso, impendulo ifihlakele de ubuze.

Ukugcina umsebenzi wakho

I akhawunti ekhululekileyo idibanisa amaphetshana kwi ncwadi nganye, irekhodi lento ogqibe ngayo, iingxaki zakho ezisoliweyo kwindawo enye, nomfundi onokuthi ubuze malunga nale phepha. IiMathematiki ngokwazo zivuliwe kubo bonke, bangeniswe okanye hayi.

Bhalisa Igama elithile

Iimpawu ezisetyenziswa apha

Nqakraza nasiphi na isibonakaliso sokuqonda okupheleleyo, umfanekiso, nokuba iileta zonke zithetha ntoni.

Indlela yokusebenza: Linear equations

  1. Start from the equation as given.
  2. Bring everything to one side and collect like terms so the right-hand side is 0.
  3. Move the constant term to the other side: subtract -4 from both sides.
  4. Divide both sides by 2, the coefficient of x.
  5. Simplify the fraction.

Imibuzo abantu bebuza

What does it mean to solve an equation?

To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.

Why do I sometimes get two answers?

A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.

How do I know whether to factor or use the quadratic formula?

Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.

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