Question 180594
Not sure what Familiarize,Translate, Carry Out, Check and State To Solve means either. But let's give it a go

Familiarize - You are given the dimensions of a rectangular box and asked to find the expression that is the volume of that box.

Translate - The volume of a rectangular box with Length L, Width W and Height H is given by {{{L * W * H}}}. The dimensions on this box are given to you as {{{W = 2x+7}}}, {{{L=5x+2}}} and {{{H=x-4}}}.

So {{{V = LWH}}}
{{{V = (5x+2)(2x+7)(x-4)}}}

Carry Out - Just grind out the math now
{{{V = (5x+2)(2x+7)(x-4)}}}
{{{V = (10x^2+35x + 4x + 14)(x-4)}}}
{{{V = (10x^2 + 39x + 14)(x-4)}}}
{{{V = 10x^3 + 39x^2 + 14x - 40x^2 - 156x - 56}}}
{{{V = 10x^3 -x^2 - 142x - 56}}}

To verify, pick a value for x and then solving for V using our equation and then solving again by finding L W and H
Let x = 5 (need to pick a value for x that makes all thee dimensions positive)
So L = 27, W=17 and H = 1. The volume is then {{{27*17*1}}} = 459

Using our equation
{{{V = 10x^3 -x^2 - 142x - 56}}}
{{{V = 10*125 - 25 - 142*5 - 56}}}
{{{V = 1250 - 25 - 710 - 56}}}
{{{V = 459}}} so it works