How do you solve #3/2+3/4a=1/4a-1/2#?

Question

Abigail Allen · Accepted Answer

See the entire solution process below:

First, subtract #color(red)(3/2)# and #color(blue)(1/4a)# from each side of the equation to isolate the #a# term while keeping the equation balanced: #3/2 + 3/4a - color(red)(3/2) - color(blue)(1/4a) = 1/4a - 1/2 - color(red)(3/2) - color(blue)(1/4a)# #3/2 - color(red)(3/2) + 3/4a - color(blue)(1/4a) = 1/4a - color(blue)(1/4a) - 1/2 - color(red)(3/2)# #0 + (3/4 - color(blue)(1/4))a = 0 - 1/2 - color(red)(3/2)# #2/4a = -4/2# Now, multiply each side of the equation by #color(red)(4)/color(blue)(2)# to solve for #a# while keeping the equation balanced: #color(red)(4)/color(blue)(2) xx 2/4a = color(red)(4)/color(blue)(2) xx -4/2# #8/8a = -16/4# #1a = -4# #a = -4#

Ethan Adkins · Answer

undefined To solve the equation $ \frac{3}{2} + \frac{3}{4}a = \frac{1}{4}a - \frac{1}{2} $, follow these steps:

1. Combine like terms on both sides of the equation.
2. Subtract $ \frac{1}{4}a $ from both sides.
3. Add $ \frac{1}{2} $ to both sides.
4. Multiply both sides by the least common denominator to clear fractions.
5. Solve for $ a $ by isolating it on one side of the equation.
6. Check the solution to ensure it satisfies the original equation.