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!