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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.

Kugwira ntchito chitsanzo · 2x + 3 = 7

Algebra · Linear-Equations

Solve 2x + 3 = 7

2 x + 3 = 7

Gawo ndi Gawo

  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.

Kusonyeza yankho
x = 2

Tsopano inu Sankhani vuto, kapena kulemba kapena kujambula wanu. Pakalipano, yankho limeneli lidzapezeka patsamba lino.

Kusunga ntchito yanu yokha

M’malo mwake, maakaunti aulere amawonjezera malemba pazophunzira zonse, mnda wa zomwe mwamaliza, mavuto anu omaliza m’malo limodzi, ndi m’bale amene mungafunse za nkhaniyo. Maphunziro a matekinoloje ndi otsegulira kwa aliyense, olembetsa kapena osalembetsa.

Kulembetsa Kulowa

Zithunzi

Pitani pa dzina lililonse lachifaniziro kuti mudziwe tanthauzo lake, chithunzi chake, ndi zimene limatanthauza.

Momwe mungagwiritsire ntchito: 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.

Mafunso omwe anthu amafunsa

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.

Zambiri pa Algebra

Quadratic equationsSystems of equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value