# How do you solve m/2-7>4?

Feb 28, 2016

$m > 22$

#### Explanation:

$\frac{m}{2} - 7 > 4$

$\frac{m}{2} > 4 + 7$

Simplify.

$\frac{m}{2} > 11$

Multiply both sides by 2.

$m > 11 \times 2$

Simplify.

$m > 22$

Feb 28, 2016

$m > 22$

#### Explanation:

Given:$\text{ } \frac{m}{2} - 7 > 4$

You treat this like a normal equation. There is one 'trap' however. If the whole thing is multiplied by a negative number the inequality is turned round the other way.

For example: It is true that $2 < 4$

Now consider the incorrect calculation of:

$\left(- 1\right) \times 2 < \left(- 1\right) \times 4 \text{ implying that } - 2 < - 4$ which is false

$- 2$ is to the right of $- 4$ on the number line so $- 2 > - 4$

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Add 7 to both sides giving

$\frac{m}{2} - 7 + 7 > 4 + 7$

$\frac{m}{2} + 0 > 11$

Multiply both sides by 2 giving

$\frac{2}{2} \times m > 2 \times 11$

But $\frac{2}{2} = 1$ giving:

$m > 22$

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