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 If a + b = -2 and x+y=-2

what is 4x + 5a + 4y + 5b?

 Aug 30, 2018
edited by Mathrules  Aug 30, 2018

Best Answer 

 #1
avatar+7350 
+2

4x + 5a + 4y + 5b

                                   Numbers can be added in any order, so we can rearrange the expression.

=  4x + 4y + 5a + 5b

                                   Now we can factor  4  out of the first two terms and  5  out of the last two terms.

=  4(x + y) + 5(a + b)   Notice that if we distributed the  4  and the  5 , we would get the last expression.

                                   Since  x + y  =  -2 ,  we can substitute  -2  in for  x + y .

=  4( -2 ) + 5(a + b)

                                   Since  a + b  =  -2 ,  we can substitute  -2  in for  a + b .

=  4( -2 ) + 5( -2 )

 

=  -8  +  -10

 

=  -18

 Aug 30, 2018
edited by hectictar  Aug 30, 2018
 #1
avatar+7350 
+2
Best Answer

4x + 5a + 4y + 5b

                                   Numbers can be added in any order, so we can rearrange the expression.

=  4x + 4y + 5a + 5b

                                   Now we can factor  4  out of the first two terms and  5  out of the last two terms.

=  4(x + y) + 5(a + b)   Notice that if we distributed the  4  and the  5 , we would get the last expression.

                                   Since  x + y  =  -2 ,  we can substitute  -2  in for  x + y .

=  4( -2 ) + 5(a + b)

                                   Since  a + b  =  -2 ,  we can substitute  -2  in for  a + b .

=  4( -2 ) + 5( -2 )

 

=  -8  +  -10

 

=  -18

hectictar Aug 30, 2018
edited by hectictar  Aug 30, 2018

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