Varia on Both Sides

Study the Example showing how to solve a linear equation

with the variable on both sides. Then solve problems 1-4.

Example

The weight of Keiko's kitten is the weight of her puppy. If each animal

gains 3 pounds, the kitten will weigh; as much as the puppy. The

equation ļw +3 = }(w + 3) describes this situation, where w is the weight

-+

of the puppy now. How much does the puppy weigh now?

6 W + 3) = 6.

3

• }(w + 3)

6 W + 3

= 2(w + 3)

W + 18 = 2w +6

w-w+ 18 = 2w - W+6

18 = w+6

12 = w

The puppy weighs 12 pounds now.

in the Example, how much will the kitten weigh if it gains 3 pounds?

Show your work

What are the digits that repeat in the smallest sequence of repeating digits in the decimal equivalent of 24/11?

What fraction is equivalent to 0.46464646··· a. 46⁄99 b. 46⁄999 c. 46⁄100 d. 23⁄50

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?