How do you solve #4(x + 0.5) = 2(x - 1.5) #?

Question

Hazel Anglin · Accepted Answer

See the entire solution process below:

First, expand the terms in parenthesis on each side of the equation: #(4 xx x) + (4 xx 0.5) = (2 xx x) - (2 1.5)# #4x + 2 = 2x - 3# Next, subtract #color(red)(2)# and #color(blue)(2x)# from each side of the equation to isolate the #x# term while keeping the equation balanced: #4x + 2 - color(red)(2) - color(blue)(2x) = 2x - 3 - color(red)(2) - color(blue)(2x)# #4x - color(blue)(2x) + 2 - color(red)(2) = 2x - color(blue)(2x) - 3 - color(red)(2)# #2x + 0 = 0 - 5# #2x = -5# Now, divide each side of the equation by #color(red)(2)# to solve for #x# while keeping the equation balanced: #(2x)/color(red)(2) = -5/color(red)(2)# #(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -2.5# #x -2.5#

Nathan Axel · Answer

undefined To solve the equation 4(x + 0.5) = 2(x - 1.5), first distribute the numbers outside the parentheses: 4x + 2 = 2x - 3. Then, isolate the variable by moving all the x terms to one side and the constant terms to the other side: 4x - 2x = -3 - 2. Simplify: 2x = -5. Finally, solve for x by dividing both sides by 2: x = -5/2 or x = -2.5.