How do you solve #(x + 1) / 4 = 2 - ( (x + 2) / 5) #?

Question

Ethan Adkins · Accepted Answer

See a solution process below:

First, multiply each side of the equation by #color(red)(20)# to eliminate the fractions while keeping the equation balanced: #color(red)(20)((x + 1)/4) = color(red)(20)(2 - ((x + 2)/5))# #cancel(color(red)(20))5((x + 1)/color(red)(cancel(color(black)(4)))) = (color(red)(20) xx 2) - (color(red)(20) xx ((x + 2)/5))# #5(x + 1) = 40 - (cancel(color(red)(20))4 xx ((x + 2)/color(red)(cancel(color(black)(5)))))# #(5 xx x) + (5 xx 1) = 40 - 4(x + 2)# #5x + 5 = 40 - (4 xx x) - (4 xx 2)# #5x + 5 = 40 - 4x - 8# #5x + 5 = -4x - 8 + 40# #5x + 5 = -4x + 32# Next, subtract #color(red)(5)# and add #color(blue)(4x)# to each side of the equation to isolate the #x# term while keeping the equation balanced: #color(blue)(4x) + 5x + 5 - color(red)(5) = color(blue)(4x) - 4x + 32 - color(red)(5)# #(color(blue)(4) + 5)x + 0 = 0 + 27# #9x = 27# Now, divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced: #(9x)/color(red)(9) = 27/color(red)(9)# #(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 3# #x = 3#

Kennedy Adams · Answer

undefined To solve the equation (x + 1) / 4 = 2 - ((x + 2) / 5), you can follow these steps:

1. Multiply both sides of the equation by 4 and 5 to eliminate the denominators:
   5 * (x + 1) = 4 * 2 - 4 * ((x + 2) / 5)

2. Simplify the equation:
   5x + 5 = 8 - 4(x + 2)

3. Distribute the -4 to the terms inside the parentheses:
   5x + 5 = 8 - 4x - 8

4. Combine like terms:
   5x + 5 = -4x

5. Add 4x to both sides of the equation:
   5x + 4x + 5 = -4x + 4x
   9x + 5 = 0

6. Subtract 5 from both sides of the equation:
   9x + 5 - 5 = 0 - 5
   9x = -5

7. Divide both sides of the equation by 9:
   (9x) / 9 = (-5) / 9
   x = -5/9

Therefore, the solution to the equation (x + 1) / 4 = 2 - ((x + 2) / 5) is x = -5/9.