Rembrandt framed his masterpiece.
The painting by itself is a rectangle with length
20
cm
20 cm20, start text, space, c, m, end text and width
16
cm
16 cm16, start text, space, c, m, end text.
The painting and frame together form a larger rectangle with length
25
cm
25 cm25, start text, space, c, m, end text and width
20
cm
20 cm20, start text, space, c, m, end text.
Find the area of the frame.
Assume no overlap between the frame and painting.

cm
2
cm
2
start text, c, m, end text, squared

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The area of the frame is 180 cm squared

Step-by-step explanation:

Area of the painting

=length⋅width

=20⋅16

=320 cm squared

Area of the painting and frame

=length⋅width

=25⋅20

=500 cm squared

Let's subtract the area of the painting from the area of the painting and the frame to find the area of just the frame:

500 - 320 = 180 cm squared

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 .