Inequalities.

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Presentation transcript:

Inequalities

Starter x < 5 ‘x is less than 5’ x ≤ 5 ‘x is less than or equal to 5’ 5 x > 7 ‘x is greater than 7’ 7 x ≥ 7 ‘x is greater than or equal to 7’ 7

Inequalities Inequalities are very similar to Equations The only difference is that you will end up with a range of values for ‘x’, rather than 1 specific value They are solved in the same way as we did equations…

Inequalities Solve the inequality below, and show the answer on a number line… ≤ 8x 32 ÷ 8 ÷ 8 ≤ x 4 1 2 3 4 5

Inequalities > > Solve the inequality below, and show the answer on a number line… > 3x 39 ÷ 3 ÷ 3 > x 13 11 12 13 14 15

Inequalities > > > Solve the inequality below, and show the answer on a number line… > 3x - 5 19 + 5 + 5 > 3x 24 ÷ 3 ÷ 3 > x 8 6 7 8 9 10

Inequalities Solve the inequality below, and show the answer on a number line… ≤ 6x + 6 36 - 6 - 6 ≤ 6x 30 ÷ 6 ÷ 6 ≤ x 5 3 4 5 6 7

Inequalities ≥ ≥ ≥ ≥ 5x + 3 10 - 2x 7x + 3 10 7x 7 x 1 Solve the inequality below, and show the answer on a number line… ≥ 5x + 3 10 - 2x + 2x + 2x ≥ 7x + 3 10 - 3 - 3 ≥ 7x 7 ÷ 7 ÷ 7 ≥ x 1 -1 1 2 3

Inequalities ≤ < < ≤ 8 4x 20 2 x 5 Write down the integers that satisfy this inequality… ≤ < 8 4x 20 ÷ 4 ÷ 4 ≤ < 2 x 5 2 3 4 5 6 Integers (whole numbers) that satisfy this inequality are: 2, 3, 4,

Inequalities < < < < 3 x - 1 8 4 x 9 Write down the integers that satisfy this inequality… < < 3 x - 1 8 + 1 + 1 < < 4 x 9 2 4 6 8 10 Integers (whole numbers) that satisfy this inequality are: 5, 6, 7, 8,

Inequalities Solve the inequality below, and show the answer on a number line… > -x 4 x by -1 x by -1 x < -4 -6 -5 -4 -3 -2 When you multiply/divide an inequality by a negative, you must reverse the sign…

Inequalities Solve the inequality below, and show the answer on a number line… ≤ 6 - 2x -5x + 2x + 2x ≤ 6 -3x ÷ -3 ÷ -3 ≥ -2 x When you multiply/divide an inequality by a negative, you must reverse the sign… -4 -3 -2 -1

Plenary What values of x satisfy both of these inequalities? Give your answer as a single inequality (draw a number line to show both – this will help!) 3x – 15 > 9 – 5x and 5x – 3 ≤ 25 + x

Summary We have learnt how to solve inequalities We have seen that inequalities give us a range of answers We have seen how to show these answers on a number line