How do you solve #4( b + 6) = 2( b + 5) + 2#?

Question

Avery Alexander · Accepted Answer

#b = -6#

#4(b+6) = 2(b+5) + 2#

To solve for the variable #b#, we need to make it by itself. First, use the distributive property (shown below) to simplify #4(b+6)# and #2(b+5)#:

Following this image, we know that:
#color(blue)(4(b+6) = (4 * b) + (4 * 6) = 4b + 24)#
and
#color(blue)(2(b+5) = (2 * b) + (2 * 5) = 2b + 10)#

Put them back into the equation:
#4b + 24 = 2b + 10 + 2#

Combine #10 + 2#:
#4b + 24 = 2b + 12#

Subtract #color(blue)(2b)# from both sides:
#4b + 24 quadcolor(blue)(-quad2b) = 2b + 12 quadcolor(blue)(-quad2b)#

#2b + 24 = 12#

Now subtract #color(blue)24# from both sides:
#2b + 24 quadcolor(blue)(-quad24) = 12 quadcolor(blue)(-quad24)#

#2b = -12#

Divide both sides by #color(blue)2#:
#(2b)/color(blue)2 = -12/color(blue)2#

Therefore,
#b = -6#

Hope this helps!

Eva Adamson · Answer

undefined To solve the equation 4(b + 6) = 2(b + 5) + 2:

1. Distribute the numbers outside the parentheses:
   4b + 24 = 2b + 10 + 2

2. Combine like terms:
   4b + 24 = 2b + 12

3. Subtract 2b from both sides:
   2b + 24 = 12

4. Subtract 24 from both sides:
   2b = -12

5. Divide both sides by 2:
   b = -6

So, the solution to the equation is b = -6.