1/6d + 2/3 = 1/4(d-2) how to solve

1 answer:

7 0

Greetings!

Solve for d.
$1/6d + 2/3 = 1/4(d-2)$
Distribute the Parenthesis.
$1/6d + 2/3 = 1/4*d+1/4*-2$
$1/6d + 2/3 = 1/4d+1/4*-2/1$
$1/6d + 2/3 = 1/4d-2/4$
Reduce.
$1/6d + 2/3 = 1/4d-1/2$
Add -2/3 to both sides.
$(1/6d + 2/3)+(-2/3)=(1/4d-1/2)+(-2/3)$
Simplify.
$1/6d=1/4d-3/6-4/6$
$1/6d=1/4d-7/6$
Add -1/4d to both sides.
$(1/6d)+(-1/4d)=(1/4d-7/6)+(-1/4d)$
Simplify.
$2/12d)-3/12d=-7/6$
$-1/12d=-7/6$
Divide both sides by -1/12.
$(-1/12d)/-1/12=(-7/6)/-1/12$
Simplify.
$d=(-7/6)*-12/1$
$d=84/6$
Reduce.
$d=14/1$
$d=14$

Hope this helps.
-Benjamin

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<h3>Square</h3>

The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.

For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.

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The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.

The area of the triangle is 24 square units.

<em>Additional comment</em>

We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.