150k views
14 votes
4: If 2(x + a) + b(x +7) = 5x + 31 what must a and b equal? a = ...... b= ....​

1 Answer

12 votes

Answer:

a = 5 and b = 3

Explanation:

2(x + a) + b(x + 7) can be simplified so that it is in the same configuration as the right side of the equation (an x term and then a constant).

2(x + a) + b(x + 7)

2x + 2a + bx + 7b

2x + bx + 2a + 7b

(2+b)x + 2a + 7b

At this point we can see that the x term on the left side of the equation is

(2+b)x and on the right side of the equation the x term is 5x. So b must be 3.

Here's an equation to show that logic.

(2+b)x = 5x

2x + bx = 5x

2x - 2x + bx = 5x -2x

bx = 3x

b = 3 if x isnot= 0

2a +7b was our constant. That was equal to 31, now we know b=3.

2a + 7b = 31

2a + 7(3) = 31

2a + 21 = 31

2a + 21 - 21 = 31 - 21

2a = 10

a = 5

User Rahul Raj
by
3.4k points