The Irregular figure can be broken into a triangle and a rectangle as shown with the dashed line.

Given:

Given that the irregular figure is broken into a triangle and a rectangle.

We need to determine the length b, the area of the triangle , the area of the rectangle and the area of the irregular figure.

Length of b:

The length of b , the base of the triangle is given by

Simplifying, we get;

Thus, the length of the base of the triangle is

Area of the triangle:

The area of the triangle can be determined using the formula,

Substituting and , we get;

Thus, the area of the triangle is 4 square feet.

Area of the rectangle:

The area of the rectangle can be determined using the formula,

where l = 5 ft, , we get;

Thus, the area of the rectangle is

Area of the irregular figure:

The area of the irregular figure can be determined by adding the area of the triangle and the area of the rectangle.

Thus, we have;

Area = Area of the triangle + Area of the rectangle

Substituting the values, we have;

Thus, the area of the irregular figure is 10.667 square feet.

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 .