How do you solve 2\leq - 4+ \frac { 8x } { 9}2≤−4+8x9?

2 Answers
MysticSmile
Sep 20, 2017

xge27/4x≥274 or 6 3/4634 or 6.756.75

Explanation:

First, we switch sides to -4+(8x)/9ge2−4+8x9≥2 and add 44 to both sides.

-4+(8x)/9color(blue)+color(blue)4ge2color(blue)+color(blue)4−4+8x9+4≥2+4.

Simplify it to be (8x)/9ge68x9≥6. Multiply both sides by 99.
(color(blue)9color(blue)*8x)/9ge6color(blue)*color(blue)99⋅8x9≥6⋅9 which is 8xge548x≥54.

Next we divide both sides by 8.

(8x)/color(blue)8ge54/color(blue)88x8≥548.

SImplify it to be xge27/4x≥274 or 6 3/4634 or 6.756.75.

Jim G.
Sep 20, 2017

x>=27/4x≥274

Explanation:

"add 4 to both sides of the inequality"add 4 to both sides of the inequality

2+4<=cancel(-4)cancel(+4)+(8x)/9

rArr6<=(8x)/9

"multiply both sides by 9"

(9xx6)<=cancel(9)xx(8x)/cancel(9)

rArr54<=8x

"divide both sides by 8"

54/8<=x

27/4<=xrArrx>=27/4

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