Using Distributive property to solve equations: distributing a silent -1 -(3x + 2) = -2x - 6 I come up with a solution of -1 but checking answer in back of book says correct answer is 1. Not sure...

Using Distributive property to solve equations: distributing a silent -1

-(3x + 2) = -2x - 6

I come up with a solution of -1 but checking answer in back of book says correct answer is 1. Not sure what I'm doing wrong.

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lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`-(3x+2)=-2x-6`

Since (3x+2) is preceded by a negative sign, it indicates that we are multiplying it by -1.

`-1(3x+2)=-2x-6`

Applying distributive property at the left side of the equation, it becomes:

`-1*3x+ (-1)*2=-2x-6`

`-3x-2=-2x-6`

Then, combine like terms.

Since -3x and -2x are on the opposite side of the equation, to combine move -2x to the left side by doing the opposite of minus.

`-3x+2x-2=-2x+2x-6`

`-3x+2x-2=-6`

`-x-2=-6`

Also, since -2 and -6 are on the opposite side of the equation, move -2 to the right side by doing the opposite of minus.

`-x-2+2=-6+2`

`-x=-6+2`

`-x=-4`

And to have x only a the left side, the negative beside x must be eliminated. To do so, divide both sides by -1.

`(-x)/(-1)=(-4)/(-1)`

`x=4`

Hence, the solution of the given equation is `x=4` .

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