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.
Kugwira ntchito chitsanzo · x^2 - 4 > 0
Gawo ndi Gawo
- 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.
Kusonyeza yankho
Tsopano inu Sankhani vuto, kapena kulemba kapena kujambula wanu. Pakalipano, yankho limeneli lidzapezeka patsamba lino.
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 KulowaZithunzi
Pitani pa dzina lililonse lachifaniziro kuti mudziwe tanthauzo lake, chithunzi chake, ndi zimene limatanthauza.
Momwe mungagwiritsire ntchito: 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.
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
Linear equationsQuadratic equationsSystems of equationsFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value