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Home > Maths I > Relationships > Solving inequalities

Maths I

Solving inequalities

Solving double inequalities

Sometimes, you are given a 'double' inequality to solve. In this case, you just do the same thing to all three parts .

Example

  • Solve:
  • -4 < 2x - 6 < 12
  • Cancel out one of the numbers, by adding or subtracting that number in all three parts of the inequality. Here we can add 6 to all the parts.
  • 2 < 2x < 18
  • Divide all three parts by the number in front of the x term.
  • Here we can divide all the parts by 2.
  • 1 < x < 9
Question

Solve the inequality \;-4 < 2x - 6 < 12

Answer
  • Add \;6 to all parts: \;2 < 2x < 18
  • Divide all parts by \;2: \;1 < x < 9

So the inequality is satisfied when \;x is between \;1 and \;9 (not including \;1 and \;9).

Now look at this question.

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