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The solution to the inequality expression is x ≥ - 5
<h3>Inequality expressions</h3>Inequality are expressions not separated by an equal sign. Given the inequality;
–4(x + 3) ≤ –2 – 2x
Expand
-4x - 12 ≤ -2 - 2x
Collect the like terms
-4x + 2x ≤ -2 + 12
-2x ≤ 10
Divide both sides by -2
-2x/-2 ≤ 10/-2
x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium.
<h3>Can this atrium be built in the rectangular plot of land?</h3>
The atrium with the <em>maximum allowable</em> radius (<em>R</em>), in feet, is represented in the image attached. The <em>real</em> atrium is possible if and only if the <em>real</em> radius (<em>r</em>) is less than the maximum allowable radius and therefore, the <em>real</em> volume (<em>V</em>), in cubic feet, must be less than than <em>maximum possible</em> volume (<em>V'</em>), in cubic feet.
First, we calculate the volume occupied by the maximum allowable radius:
<em>V' =</em> (8 · π / 3) · (45 ft)³
<em>V' ≈</em> 763407.015 ft³
The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium.
To learn more on volumes, we kindly invite to check this verified question: brainly.com/question/13338592
