The width of a rectangle is 3 1/2 inches, and the length is 4 3/4 inches. What is the area of the rectangle?

16  5/8  in^2

Step-by-step explanation:

The area of a rectangle is found by

A = l*w

  = 3 1/2 * 4 3/4

Changing to improper fractions

  = (2*3+1)/2  * (4*4+3)/4

  = 7/2 * 19/4

     133/8

Changing back to a mixed number

8 goes into 133 16 times with 5 left over

16  5/8

16.625 in²

Step-by-step explanation: We can find the area of a rectangle using the formula that is shown below.

Area = length · width

Since the length is 4 and 3/4 inches and the width is 3 and 1/2 inches, we can plug this information into the formula to get .

From here, we need to rewrite 4 and 3/4 and 3 and 1/2 as either improper fractions or decimals in order to multiply.

I would suggest rewriting 4 and 3/4 as the decimal 4.75

and 3 and 1/2 as the decimal 3.5.

So we have (4.75 in.)(3.5 in.) which simplifies to 16.625 in².

So the area of the rectangle is 16.625 in².

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .