# How do you graph and solve 2-x<=3-(5x-4)?

Jul 31, 2018

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The given inequality

color(red)(2-x<=3-(5x-4)

can be simplified to

color(blue)(x<=5/4

#### Explanation:

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How do we graph and solve color(red)(2-x<=3-(5x-4) ?

We will try to simplify the inequality first before graphing:

color(blue)(2-x<=3-(5x-4)

Remove the parenthesis:

$\Rightarrow 2 - x \le 3 - 5 x + 4$

Combining like terms and simplifying:

$\Rightarrow 2 - x \le 7 - 5 x$

Add color(red)(5x to both sides of the inequality:

$\Rightarrow 2 - x + 5 x \le 7 - 5 x + 5 x$

$\Rightarrow 2 + 4 x \le 7 - \cancel{5 x} + \cancel{5 x}$

Rearrange the terms and simplify:

$\Rightarrow 4 x + 2 \le 7$

Subtract color(red)(2 from both sides of the inequality:

$\Rightarrow 4 x + 2 - 2 \le 7 - 2$

$\Rightarrow 4 x + \cancel{2} - \cancel{2} \le 7 - 2$

$\Rightarrow 4 x \le 5$

Divide both sides of the inequality by color(red)(4

$\Rightarrow 4 x \le 5$

$\Rightarrow \frac{4 x}{4} \le \frac{5}{4}$

$\Rightarrow \frac{\cancel{4} x}{\cancel{4}} \le \frac{5}{4}$

color(red)(x<=5/4

This is our simplified inequality.

We can graph this inequality as shown below:

The solid line in the graph indicates the value color(blue)([x=(5/4)] that is part of the final solution.

Hope it helps.