How do you solve #|5x-4| +3 = 3#?

Question

Eva Adamson · Accepted Answer

See the solution process below:

First, subtract #color(red)(3)# from each side of the equation to isolate the absolute value function while keeping the equation balanced: #abs(5x - 4) + 3 - color(red)(3) = 3 - color(red)(3)# #abs(5x - 4) + 0 = 0# #abs(5x - 4) = 0# Normally an absolute value equality would produce two answers. However, because the absolute value function is equal to #0# there is only one solution. We can equate the term within the absolute value to #0# and solve for #x#: #5x - 4 = 0# #5x - 4 + color(red)(4) = 0 + color(red)(4)# #5x - 0 = 4# #5x = 4# #(5x)/color(red)(5) = 4/color(red)(5)# #(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 4/5# #x = 4/5#

Savannah Anderson · Answer

undefined To solve the equation $ |5x - 4| + 3 = 3 $, you first subtract 3 from both sides to isolate the absolute value term, leaving $ |5x - 4| = 0 $. Then, you solve the absolute value equation $ |5x - 4| = 0 $ by setting the expression inside the absolute value bars equal to zero: $ 5x - 4 = 0 $. Solving for x, you get $ x = \frac{4}{5} $.

Eva Adamson · Answer

undefined To solve the equation |5x - 4| + 3 = 3:

1. Subtract 3 from both sides of the equation:

|5x - 4| = 0.

2. Now, the absolute value equals zero, which means the expression inside the absolute value must be zero.

3. Solve the equation 5x - 4 = 0:

5x - 4 = 0
5x = 4
x = 4/5.

So, the solution to the equation |5x - 4| + 3 = 3 is x = 4/5.