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3 years ago

Solve the equation shown for x. 2/3 x -4 1/2 = -8

2 answers:

5 0

X = - 21/4

2/3x - 4 1/2 = - 8
2/3x = - 8 + 4 1/2

- 8 + 4 = - 4. Then do - 4 + 1/2 = - 3 1/2

2/3x = - 3 1/2

- 3 1/2 is the same as = - 7/2

2/3x = - 7/2

Flip the coefficient on the variable and multiply both sides by it.

(3/2)(2/3)x = - 7/2(3/2)

x = - 7/2(3/2)

x = - 21/4

liq [111]3 years ago

4 0

The answer would be -5 1/4

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The length of a rectangular photo is 1 centimeter less than three times its width. If the area of the photo is 102 square centim

noname [10]

Answers:

Length = 17
Width = 6

======================================================

How to get those answers:

Let w be the unknown width in centimeters. This variable is some positive real number. This means w > 0 which will be useful later.

The length is "1 cm less than 3 times its width" and it tells us the length is defined by the expression 3w-1. Whatever w is, we triple it to get 3w and then subtract 1 to get the final length.

Multiply the length and width to get the area 102

length*width = area

(3w-1)*w = 102

3w^2-w = 102

3w^2-w-102 = 0

We could guess and check our way to factoring this, but that's not very efficient. The quadratic formula is the better option. It may seem a bit messy, but it's a more direct path that doesn't involve guessing.

$w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-102)}}{2(3)}\\\\w = \frac{1\pm\sqrt{1225}}{6}\\\\w = \frac{1\pm35}{6}\\\\w = \frac{1+35}{6}\ \text{ or } \ w = \frac{1-35}{6}\\\\w = \frac{36}{6}\ \text{ or } \ w = \frac{-34}{6}\\\\w = 6\ \text{ or } \ w \approx -5.667\\\\$

We ignore the second solution (w = -5.667 approximately) because we stated earlier that w > 0. In other words, a negative length does not make sense, so that's why we ignore it.

-----------------

If w = 6 cm is the width, then 3w-1 = 3*6-1 = 18-1 = 17 cm is the length.

Note that length*width = 17*6 = 102 which is the proper area we want. This confirms the answers.

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3 years ago