How do you solve #4 (2x - 1/2) = -6 (2/3x + 1/2)#?

Question

How do you solve #4 (2x - 1/2) = -6 (2/3x +  1/2)#?

Nathan Axel · Accepted Answer

See a solution process below:

First, multiply each term inside the parenthesis by the term outside the parenthesis to expand the terms in parenthesis on each side of the equation: #color(red)(4)(2x - 1/2) = color(blue)(-6)(2/3x + 1/2)# #(color(red)(4) * 2x) - (color(red)(4) * 1/2) = (color(blue)(-6) * 2/3x) + (color(blue)(-6) * 1/2)# #8x - 2 = -12/3x + (-3)# #8x - 2 = -4x - 3# Next, add #color(red)(2)# and #color(blue)(4x)# to each side of the equation to isolate the #x# term while keeping the equation balanced: #color(blue)(4x) + 8x - 2 + color(red)(2) = color(blue)(4x) - 4x - 3 + color(red)(2)# #(color(blue)(4) + 8)x - 0 = 0 - 1# #12x = -1# Now, divide each side of the equation by #color(red)(12)# to solve for #x# while keeping the equation balanced: #(12x)/color(red)(12) = -1/color(red)(12)# #(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = -1/12# #x = -1/12#

Jace Anderson · Answer

undefined To solve the equation 4(2x - 1/2) = -6(2/3x + 1/2), follow these steps:

1. Distribute the terms inside the parentheses:
   8x - 2 = -4x - 3

2. Combine like terms by adding 4x to both sides:
   12x - 2 = -3

3. Add 2 to both sides to isolate the variable term:
   12x = -1

4. Divide both sides by 12 to solve for x:
   x = -1/12