Inequalities - KS3 Maths - BBC Bitesize (2024)

Key points

Inequalities - KS3 Maths - BBC Bitesize (1)

  • Inequalities are used to describe the relationship between expressions that are not equal. They can be presented algebraically, in words, or on a number line.

  • The two sides in an are equal. This is not the case in an inequality, as one side may be greater than (or less than) the other.

  • An inequality can have multiple solutions. When a single inequality is used there can be an number of solutions. In some cases, the number of solutions can be . For example, when the unknown value is an and between two given values.

  • Solutions to an inequality may be given as a simplified inequality, a finite list of values, a or as an illustration on a number line.

Inequalities - KS3 Maths - BBC Bitesize (2)

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Video

Watch the video to learn how Shahan, a video games developer, uses inequalities in his work and find out why inequalities are important when it comes to designing new video games.

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Understanding and using inequality symbols

Inequality symbols are used when values are not equal.

The used when writing inequalities is: ≠, <, ≤, > or ≥, where:

  • means ‘not equal to’
  • < means ‘less than’
  • > means ‘greater than’
  • means ‘less than or equal to’
  • means ‘greater than or equal to’

Examples

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  1. Inequalities - KS3 Maths - BBC Bitesize (3)

Slide 1 of 9, In a box in the top left is the phrase inequality symbols. A symbol with two short lines joined together at the left and sloping diagonally apart to the right – this is labelled less than. To its right, the same symbol with a horizontal line underneath – this is labelled less than or equal to. Underneath, a symbol with two short parallel lines and a diagonal line sloping up from left to right through the two lines – this is labelled not equal to. Underneath, a symbol with two short lines which slope diagonally from left to right to join at the right – this is labelled greater than. To its right, the same symbol with a horizontal line underneath – this is labelled greater than or equal to., The inequality symbols are used when values are not equal.

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Which inequality is used to state that 𝒏 is at least 8?

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Inequalities on a number line and listing integer solutions

Inequalities can be illustrated on a .

  • For a single inequality, with one value:
  1. Draw a circle above the value on the number line.

    • The circle is unshaded for < and >
    • The circle is shaded for ≤ and ≥
  2. Draw a horizontal line with an arrow in the same direction as the inequality:

    • to the left with an arrow for < and ≤
    • to the right with an arrow to the right for > and ≥

For a single inequality there are an infinite number of integer solutions. These can’t be listed in a solution set.

  • For an inequality with two values:
  1. Draw circles above the values on the number line.

    • The circle is unshaded for < and >
    • The circle is shaded for ≤ and ≥
  2. Draw a horizontal line between the circles.

For an inequality with two values there are a finite number of integer solutions. This can be written as a solution set which is presented in curly brackets. For example, {2, 3, 4}.

Examples

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  1. Inequalities - KS3 Maths - BBC Bitesize (4)

Slide 1 of 10, Three inequalities with number lines increasing in ones from left to right from minus two to four – these are labelled n. The first, n is greater than minus one. A circle is above minus one on the number line – it is unshaded. An arrow points from the circle to the right along the number line. The second inequality, n is less than or equal to three. A circle is above three on the number line – it is shaded black. An arrow points from the circle to the left along the number line. The third inequality, minus one is less than n which is less than three. A circle is above minus one on the number line – it is unshaded. A circle is above three on the number line – it is unshaded. A line joins the two circles., A number line can be used to illustrate an inequality.

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Question

What inequality is shown on the number line?

Inequalities - KS3 Maths - BBC Bitesize (5)

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Solving simple linear inequalities

A single inequality written with an may be solved by using :

  1. Undo each process in the inequality by using the inverse operation. Inverse operations include addition and subtraction, and multiplication and division.

  2. Start with the last operation and work back to the first.

  3. For each step make sure that the inverse is applied to both sides of the inequality.

  4. Once the variable is write the solution as a simple inequality.

An expression between inequalities is solved using inverse operations in the same way:

  • Apply each inverse operation to all three parts of the inequality.
  • Write the solution as a variable between two inequalities.

Examples

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  1. Inequalities - KS3 Maths - BBC Bitesize (6)

Slide 1 of 10, Example one. An inequality – three n is greater than or equal to twenty four., Solve the inequality 3𝒏 ≥ 24

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Question

Solve the inequality and list the integer solutions for 𝒏

Inequalities - KS3 Maths - BBC Bitesize (7)

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Practise using inequalities

Quiz

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Game - Divided Islands

Divided Islands. gameDivided Islands

Use your maths skills to help the islanders of Ichi build bridges and bring light back to the islands in this free game from BBC Bitesize.

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Inequalities - KS3 Maths - BBC Bitesize (2024)
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