How do you solve for x in #2x+9= 7x-1#?

1 Answer
Mar 11, 2016

Answer:

#color(green)(x=2)#

With practice you will be able to cut out a lot of the steps I have shown you!

Explanation:

#color(blue)("Method")#

manipulate so that you have all the x's and their coefficients on one side of the = and all the numbers on the other

Manipulate the x's so that you end up with just a single x and everything else on the other side of the =

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#color(blue)("Solving your question")#

Given:#" "color(brown)(2x+9=7x-1)#

Keep #7x# where it is but move the #2x# as #7x-2x# is positive

Subtract #color(blue)(2x)# from both sides

#" "color(brown)(2x+9color(blue)(-2x)=7x-1color(blue)(-2x))#

#" "color(brown)(0+9=7x-2x-1#

#" "color(brown)(9=5x-1#

Add #color(blue)(1)# to both sides

#" "color(brown)(9color(blue)(+1)=5x-1color(blue)(+1)#

#" "color(brown)(10=5x+0)#

Write as: #color(brown)(5x=10)" "# ( this is done to match convention)

Divide both sides by #color(blue)(5)#

#" "color(brown)( (5x)/(color(blue)(5)) =10/(color(blue)(5))#

#" "color(brown)( 5/5 x =2#

But #5/5=1# giving

#color(green)(x=2)#