How do you solve $7- x \geq - x + 7( x - 4)$ ?

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Answer 1 · 2018-06-25T16:17:56

$x <= 5$

Here's how I did it:

$7-x >= -x + 7(x-4)$

Distributive the right hand side:
$7-x >= -x + 7x - 28$

Combine $color(blue)(-x)$ and $color(blue)(7x)$ :
$7-x >= 6x - 28$

Add $color(blue)x$ to both sides of the inequality:
$7-x quadcolor(blue)(+quadx) >= 6x - 28 quadcolor(blue)(+quadx)$

$7 >= 7x - 28$

Add $color(blue)28$ to both sides:
$7 quadcolor(blue)(+quad28) >= 7x - 28 quadcolor(blue)(+quad28)$

$35 >= 7x$

Divide both sides by $color(blue)7$ :
$35/color(blue)7 >= (7x)/color(blue)7$

$5 >= x$

Therefore, $x <= 5$ .

Hope this helps!

How do you solve 7- x \geq - x + 7( x - 4)7- x \geq - x + 7( x - 4)?