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3 years ago

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

Mathematics

1 answer:

expeople1 [14]3 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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Answer:

Each bracelet has 12 small charms and 5 large charms

Each order also gets<em> </em>5 blank spacer charms to use to separate charms or fill in the bracelet.

(a) 17x + 5 = y

17 charms are needed for each bracelet plus 5 blank spacer charms that come with each order.

(b) the order she is filling needs 158 charms. How many bracelets were purchased in this order?

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Let's solve your equation

17x+5=158

Subtract 5 from both sides.

17x+5−5=158−5

17x=153

Divide both sides by 17.

17x / 17 = 153 / 17

x=9

9 bracelets were purchased in this order.

(c) Toby says they don’t have enough charms to fill an order that needs 264 charms. Sarah says it’s not possible for an order to need 264 charms.

17x + 5 = y

17x + 5 = 264

Subtract 5 from both sides.

17x + 5 -5 = 264-5

17x = 259

Divide both sides by 17.

17x / 17 = 259 / 17

x = 15.235

Sarah is wrong because 264 charms can make about 15 bracelets.

Step-by-step explanation:

I hope this helps

Have a nice day!!

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Step-by-step explanation:

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