The length of a rectangular garden is 2x and it’s width is x-3. the garden’s area is 80ft^2. find the dimensions

The dimensions of the garden are 5 by 16 units

Step-by-step explanation:

The area of a rectangle is A = L * W.  Here, (2x)*(x - 3) = 80 ft².

Let's multiply this result out and put it into standard quadratic form:

2x² - 6x - 80 = 0.

Dividing this entire equation through by 2 simplifies it to

x² - 3x - 40 = 0.  Factors of 40 are 10 and 4, 8 and 5, and so on.

Note how 5 - 8 = -3, which matches the coefficient of the x term.  Thus, in factored form this quadratic is

(x - 8)(x + 3) = 0, so that x = 8 or x = -3.  Discard the negative root, since we're discussing real life measurements.

Then the dimensions of the garden are :  L  = 2x = 2(8) = 16, and

W = x - 3 = 8 - 3 = 5.

Check:  does 5 * 16 = 80?  YES

The dimensions of the garden are 5 by 16 units.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

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