Solving Inequalities
We can solve inequalities in the same way as we solved equations.
Example 1
| Solve |
2y + 3 > 15 |
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(– 3) |
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2y > 12 |
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(÷ 2) |
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y > 6 |
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y > 6 is the solution, showing that the following are possible integer values of y: 7, 8, 9, 10 ..................
Example 2
| Solve |
3y – 6 ≤ 9 |
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(+ 6) |
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3y ≤ 15 |
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(÷ 3) |
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y ≤ 5 |
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In this case, we include 5 in the solution because of the ≤ sign.
The possible integer values of y are: 5, 6, 7, 8, 9..........
If the term in y is negative, always move it to the other side and make it positive, as in the following example.
Example 3
| Solve |
5 – 2y > 3 |
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(+ 2y) |
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5 > 3 + 2y |
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2 > 2y |
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(÷ 2 ) |
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1 > y |
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We read an inequality from the letter side so this reads 'y is less than 1' (y < 1).
The possible values of y are 0, –1, –2, –3...........
Note what to do if two inequality signs are used, as in the following case.
Example 4
Solve |
3x – 1 > 2x < x + 5. |
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In this instance, we split them up.
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3x – 1 > 2x |
and |
2x < x + 5 |
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3x – 2x >1 |
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2x – x < 5 |
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x >1 |
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x < 5 |
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The possible values of x are 2, 3, 4.
The solution to an inequality is called 'the range of values'.
Inequalities can be plotted graphically (See the study note on graphs).
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