(6x-8) - (5x+9) =3solve for x

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msrobinsonlovesalgebra's profile pic

msrobinsonlovesalgebra | High School Teacher | (Level 1) Adjunct Educator

Posted on

grumpybear -- You know how to do the distributive property I would assume . . so you will use it to get rid of the paratheses in the problem.

Is there anything in front of the first set of ()'s?  This would make them a little unneccessary . . so just drop them. 

Now in front of the second set is only a - . . .think of this as a -1 (because there is always an invisible 1 if there is nothing in that spot, right?)  So, distribute the -1 into the second set of ()'s.  Now you will have . . .

6x - 8 - 5x - 9 = 3  -->  {-1(5x) + -1(9) = -5x - 9}

from here, combine like terms (x's with other x's & #'s with other #'s) on the same side of the equal sign.

6x - 5x = 1x or just x (there's the invisible 1 again)

-8 - 9 = -17

so . .

x - 17 = 3      This is looking a little easier to handle right!

   +17     +17    add 17 to both sides to cancel it from the x

x        =  20

Distributing the negative problems (like this one) can be a little tricky.  Remember to check your answers to make sure you are right . . .use your calculator to make it quick and easy to check . . .

(6*20 - 8) - (5*20 + 9) = ?

(112) - (109) = 3

 

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

(6x-8) - (5x+9) = 3                 (open brackets)

6x - 8 - 5x - 9 =3

x - 8 - 9 =3                             (subtract)

x - 17 = 3                         

x - 17 + 17 = 3 + 17                (adding 17 on both sides)

x = 20 Answer 

You can verify it by plugging the value of x in the above equation.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

This is an  equation  in one variable x. Such equations could be solved by simple operations like, adding equal quantity or subtracting equal quantity , mutiplying or dividing by equal quantity  both sides.(But remember we do not divide by zero)

(6x-8)-(5x+9)=3

Open the bracket.There is no difficulty in opening the first bracket as it does not change contents inside the bracket. While opening the second bracket see that - sign outside acts as mutiplication by (-1) and is distributive over  the terms 5x and 9 inside the bracket.

6x-8-1(5x)-1(9)=3

6x-8-5x-9=3.

Collect similar or like terms.

6x-5x-8-9=3

Simplify.

x-17=3

Add 17 to both sides.

x-17+17=3+17

x=20

 

Now verify  whether  x=20 satisfies  the given equation:

Left side: (6*20-8)-(5*20-9) =(120-8)-(100+9)=112-109=3.

Right side:3.

 

 

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

(6x - 8) - (5x + 9) = 3

Removing the brackets in the equation we get:

6x - 8 - 5x - 9  = 3

Therefore: x - 17 = 3

Adding 17 to both sides of equation we get:

x = 3 + 17 = 20

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