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Introduction to Equations and Inequalities

Plot ordered pairs in a Cartesian coordinate system.

Introduction to Equations and Inequalities

Irrigation is a critical aspect of agriculture, which can expand the yield of farms and enable farming in areas not naturally viable for crops. But the materials, equipment, and the water itself are expensive and complex. To be efficient and productive, farm owners and irrigation specialists must carefully lay out the network of pipes, pumps, and related equipment. The available land can be divided into regular portions (similar to a grid), and the different sizes of irrigation systems and conduits can be installed within the plotted area.

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Comment faire: Introduction to Equations and Inequalities

  1. Plot ordered pairs in a Cartesian coordinate system.
  2. Graph equations by plotting points.
  3. Graph equations with a graphing utility.
  4. Find x-intercepts and y-intercepts.
  5. Use the distance formula.
  6. Use the midpoint formula.

Questions posées par les gens

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.

Certaines parties de cette page sont adaptées de OpenStax College Algebra 2e (CC BY-NC-SA 4.0). Condensés et réexpliqués ici ; les erreurs sont les nôtres. Comme sa source est autorisée à des fins non commerciales, cette leçon est gratuite, ne vend rien et est partagée avec la même licence.

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Linear equationsQuadratic equationsSystems of equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value