State the mathematical properties of all the steps in the equation below. (2x + 3) − 7 = 8 + x Problem Statement.
(2x + 3) + (−7) = 8 + x
((2x + 3) + (−7)) + 7 = (8 + x) + 7
(2x + 3) + (−7 + 7) = (8 + x) +7
(2x + 3) + 0 = (8 + x) + 7
2x + 3 = (8 + x) + 7
2x + 3 = 7 + (8 + x)
2x + 3 = (7 + 8) + x
2x + 3 = 15 + x
(2x + 3) + (−3) = (15 + x) + (−3)
2x + (3 + (−3)) = (15 + x) + (−3)
2x + 0 = (15 + x) + (−3)
2x = (15 + x) + (−3)
2x = (−3) + (15 + x)
2x = (−3 + 15) + x
2x = 12 + x
2x + (−x) = 12 + x + (−x)
2x + (−x) = 12 + 1 · x + (−x)
2x + (−x) = 12 + 1 · x + (−1) · x
2x + (−x) = 12 + (1 + (−1))x
2x + (−x) = 12 + 0 · x
2x + (−x) = 12 + 0
2x + (−x) = 12
2x + (−1) · x = 12
(2 + (−1)) · x = 12
1 · x = 12
x = 12 Solution

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?