Solve the inequality. Enter any fractions as reduced improper fractions. 4x ≤ -2/5(6x + 6) The solution is _____

Mathematics

1 answer:

Deffense [45]3 years ago

6 0

Answer:

x≤ -3/8

Step-by-step explanation:

$4x\le \:-\frac{2}{5}\left(6x+6\right)\\$

Expand ;

$\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}$

$4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x$

Simplify

$\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}$

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We are given a rectangular prism.
A rectangular prism is no different than a cuboid.
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The width of the rectangular prism is "h+5".
The volume of the rectangular prism is the same as that of the cuboid.
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