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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.
Kushanda muenzaniso · 2x + 3 = 7
Step by step
- 2 x + 3 = 7
Start from the equation as given.
- 2 x - 4 = 0
Bring everything to one side and collect like terms so the right-hand side is 0.
- 2 x = 4
Move the constant term to the other side: subtract -4 from both sides.
- x = \frac{4}{2}
Divide both sides by 2, the coefficient of x.
- x = 2
Simplify the fraction.
Kuratidza mhinduro
Zvino iwe Choose a problem, or type or draw your own. Every step, a picture, the answer hidden until you ask.
Mubhadharo wakasununguka unowedzera mazita ezvidzidzo, zvinyorwa zvezvidzidzo zvawakati wazvigadzirira, zvidzidzo zvawave uchizvigadzirisa, uye mudzidzisi waungabvunza nezvechidzidzo ichi. Maths inowanikwa kune vese, vasiri vadzidzi kana vadzidzi. Kuwana mazita ezvidzidzo zvinodiwa kunogona kuitwa pawebsite ye Maths.
Kutanga KupindaMazita anoshandiswa pano
Tinya chero chiratidzo kuti uone chirevo chakazara, vhidhiyo, uye kuti chii chinoreva chero chiratidzo.
Maitiro: Linear equations
- Start from the equation as given.
- Bring everything to one side and collect like terms so the right-hand side is 0.
- Move the constant term to the other side: subtract -4 from both sides.
- Divide both sides by 2, the coefficient of x.
- Simplify the fraction.
Mabvunzo vanhu vanobvunza
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.
More in Algebra
Quadratic equationsSystems of equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value