An inequality is solved like an equation, find where the expression is zero, and then a sign test on each interval between those critical points decides which intervals belong to the answer. The shaded region in the graph is the solution set.
Gumagana halimbawa · x^2 - 4 > 0
Hakbang-hakbang
- x^{2} - 4 > 0
Start from the inequality.
- x^{2} - 4 > 0
Move everything to the left so we compare against 0.
- x = -2, x = 2
Find the critical points: where the expression equals 0 (or is undefined). They split the number line into test intervals.
- (-\infty,\, -2): +\;\;(-2,\, 2): -\;\;(2,\, \infty): +
Test a point inside each interval to find the sign of the expression there.
- \left(-\infty, -2\right) \cup \left(2, \infty\right)
Keep the intervals whose sign satisfies the inequality (closed endpoints for ≤ / ≥, open for < / >).
- \left(-\infty < x \wedge x < -2\right) \vee \left(2 < x \wedge x < \infty\right)
The same answer written as inequalities.
Ipahayag ang sagot
Ngayon ikaw Pumili ng isang problema, o i-type o gumuhit ng iyong sarili. Sa bawat hakbang, isang larawan, ang sagot na nakatago hanggang sa hilingin mo.
Ang isang libreng account ay nagdaragdag ng mga tala sa bawat aralin, isang tala ng kung ano ang iyong natapos, ang iyong mga nalulutas na problema sa isang lugar, at isang guro na maaari mong tanungin tungkol sa pahinang ito. Ang matematika mismo ay bukas sa lahat, naka-sign in o hindi.
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Paano: Inequalities
- Start from the inequality.
- Move everything to the left so we compare against 0.
- Find the critical points: where the expression equals 0 (or is undefined). They split the number line into test intervals.
- Test a point inside each interval to find the sign of the expression there.
- Keep the intervals whose sign satisfies the inequality (closed endpoints for ≤ / ≥, open for < / >).
- The same answer written as inequalities.
Mga katanungan na tanong ng mga tao
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.
Higit pa sa Algebra
Linear equationsQuadratic equationsSystems of equationsFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value