# How do you solve and graph 10-x>=3?

Feb 26, 2017

$x \le 7$

#### Explanation:

Using a shortcut tick

To make the $x$ positive multiply both sides by (-1). However, in doing this the inequality sign must be turned round the other way.

$\textcolor{g r e e n}{10 - x \ge 3 \text{ "->" } - 10 + x \le - 3}$

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$\textcolor{b r o w n}{\text{Why does the sign turn round?}}$

Using first principles

$10 - x \ge 3$

Add $x$ to both sides

$10 + 0 \ge 3 + x$

Subtract 3 from both sides

$10 - 3 \ge x$

this is the same as:

$x \le 10 - 3$

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$\textcolor{b r o w n}{\text{Continuing the solution}}$

Add 10 to both sides

color(green)(-10+x<=-3" "->" "0+x<=10-3

$\textcolor{g r e e n}{x \le 10 - 3 \text{ "->" } x \le 7}$