What is the solution to the linear equation?

d – 10 – 2d + 7 = 8 + d – 10 – 3d

Step-by-step explanation:

Simplifying

d + -10 + -2d + 7 = 8 + d + -10 + -3d

Reorder the terms:

-10 + 7 + d + -2d = 8 + d + -10 + -3d

Combine like terms: -10 + 7 = -3

-3 + d + -2d = 8 + d + -10 + -3d

Combine like terms: d + -2d = -1d

-3 + -1d = 8 + d + -10 + -3d

Reorder the terms:

-3 + -1d = 8 + -10 + d + -3d

Combine like terms: 8 + -10 = -2

-3 + -1d = -2 + d + -3d

Combine like terms: d + -3d = -2d

-3 + -1d = -2 + -2d

Solving

-3 + -1d = -2 + -2d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '2d' to each side of the equation.

-3 + -1d + 2d = -2 + -2d + 2d

Combine like terms: -1d + 2d = 1d

-3 + 1d = -2 + -2d + 2d

Combine like terms: -2d + 2d = 0

-3 + 1d = -2 + 0

-3 + 1d = -2

Add '3' to each side of the equation.

-3 + 3 + 1d = -2 + 3

Combine like terms: -3 + 3 = 0

0 + 1d = -2 + 3

1d = -2 + 3

Combine like terms: -2 + 3 = 1

1d = 1

Divide each side by '1'.

d = 1

Simplifying

d = 1

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

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