Less Than

If x is zero, is the following true?

9x + 18 < 5x + 2 < 2x + 2

In the back of your books write down at least 10 values of x which satisfy this inequality statement.

"<" means "is less than"


Topics: Starter | Algebra

  • Transum,
  • This quite an advanced mathematical statement but sometimes it is effective for pupils to learn about a concept by unpicking a more complex problem rather than starting with the very simplest examples. A little 'trial and improvement' is expected though of course those with experience of solving inequalities may choose to solve the problem in the way the answer is presented below.
  • John Tranter,
  • Never smile at a crocodile,
    Beware its welcome grin,
    Don't stand too close to its open mouth
    in case you topple in!
    If the open mouth faces to the left,
    Remember this you might,
    The number there is bigger than
    the number to the right.
    If the open mouth faces to the right,
    Learn this fact by heart,
    The number there is bigger than
    the number at the start.

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When x is zero the statement is not true.
Here are ten values of x which make the statement true:
-5, -6, -7, -8, -9, -10, -11, -12, -13, -14,
there are of course many other values which make the statement true.

An inequality like this can be solved by splitting it into two parts:

9x + 18 < 5x + 2
4x < -16
x < -4
5x + 2 < 2x + 2
3x < 0
x < 0

So the complete answer is x < -4

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