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2 years ago

Are the equations 6x-6=3x and x-1=3x equivalent?

Mathematics

1 answer:

expeople1 [14]2 years ago

4 0

Answer:

No, they aren't the same (equivalent).

Step-by-step explanation:

First, solve for both equations:

<u>Equation #1</u>: <em>6x-6=3x </em>

Simplifying

6x + -6 = 3x

Reorder the terms:

-6 + 6x = 3x

Solving

-6 + 6x = 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.

-6 + 6x + -3x = 3x + -3x

Combine like terms: 6x + -3x = 3x

-6 + 3x = 3x + -3x

Combine like terms: 3x + -3x = 0

-6 + 3x = 0

Add '6' to each side of the equation.

-6 + 6 + 3x = 0 + 6

Combine like terms: -6 + 6 = 0

0 + 3x = 0 + 6

3x = 0 + 6

Combine like terms: 0 + 6 = 6

3x = 6

Divide each side by '3'.

x = 2

Simplifying

<u>Equation #2</u><em>: </em><em>x-1=3x</em>

Simplifying

x + -1 = 3x

Reorder the terms:

-1 + x = 3x

Solving

-1 + x = 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.

-1 + x + -3x = 3x + -3x

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

-1 + -2x = 3x + -3x

Combine like terms: 3x + -3x = 0

-1 + -2x = 0

Add '1' to each side of the equation.

-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0

0 + -2x = 0 + 1

-2x = 0 + 1

Combine like terms: 0 + 1 = 1

-2x = 1

Divide each side by '-2'.

x = -0.5

Simplifying

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Are the equations 6x-6=3x and x-1=3x equivalent?​

Are the equations 6x-6=3x and x-1=3x equivalent?