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Summary

  • Two real numbers or two algebraic terms (expressions) connected by form an inequality.
  • For solving algebraically, equal numbers may be added or subtracted to both sides of an inequality.
  • Both sides of an inequality can be multiplied or divided by the same positive quantity.
  • If both sides are multiplied by a negative quantity, the inequality sign changes.
  • The solution of an inequality is the value/s of which satisfies the inequality.
  • The solution can be represented on a number line by marking the point either darkly (if that point is included) or drawing a circle around it (if it is excluded) and drawing a dark line to the right or left of that point according to the solution.
  • If there are two variables in the inequality, then the line graph corresponding to the equality is drawn; then the area to the right, left, top or bottom of the line is shaded as the case may be (after verifying by substituting a known point (a, b)).
  • If the inequality is of the form or then the points on the line are also included in the solution; so the line is drawn continuously dark.
  • If the inequality of the form or , then the points on the line are not included in the solution; so the line is drawn as dotted line.
  • The solution region of a number of linear inequalities in two variables is the region that is common to all the individual solution regions.




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