precalculus

posted by .

solve the inequality algebraically. write the solution in interval notation.
the absolute value of x-2/3 is less than or equal to 4

  • precalculus -

    |x - 2/3| <= 4

    if x - 2/3 >= 0 then |x - 2/3| = x - 2/3

    In that case,

    x - 2/3 <= 4
    x <= 14/3 and x >= 2/3 (remember x - 2/3 >= 0)

    so, x is in [2/3 , 14/3]

    if x - 2/3 >= 0 then |x - 2/3| = -(x - 2/3)

    In that case,

    2/3 - x <= 4
    x >= -10/3
    But x - 2/3 < 0 means x < 2/3
    So,
    x is in [-10/3 , 2/3)

    So, finally, x is in [-10/3 , 2/3)U[2/3 , 14/3]
    or, x is in [-10/3 , 14/3]

    This makes sense. Think of the graph of |x|. It is a V shape. If |x| < k, then you want the part of the V below the line y=k.

    In this case, the V is shifted 2/3 to the right, and we want the part of the V below the line y=4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra II

    I need some help with some problems as well as need some checked. Could you please help me?
  2. absolute value inequality help

    solve and write in interval notation |6x+2|<18 -18<6x+2<18 10/3<x<8/3 (-10/3,8/3)
  3. Algebra

    Right now we are learning about absolute value inequalities. I have to solve and graph this inequality: Pretend my paranpheses are absolute value signs (x-4) + 5 is greater than or equal to 10. I assume I would take 5 away from each …
  4. Algebra

    solve each inequality algebraically and give the answer by using interval notation. 5-9y <_ (less than or equal to) 19-2y I got -2y <_ (less than or equal to) y; (-2, infinity]. But the back of the book answer says [infinity, …
  5. Math

    Solve the inequality by first rewriting it as an equivalent inequality without absolute value bars. Express solution set using interval notation. | x+3 | +8 is less than or equal to 14 Thanks so much for helping me!
  6. calculus

    solve the following inequality. write your solution in interval notation. x^3+9x^2-108 less than or equal to 0
  7. calculus

    solve the following inequality. write your solution in interval notation. x^3+9x^2-108 less than or equal to 0 please show all work
  8. algebra URGENT HELP

    analyze the graph of the following function solve R(x)=x(x-16)^2 /(x+11) solve the following inequality write solution in interval notation x+14/x-8 less than or equal to 1
  9. SAT math

    1. x>15-2x / -3 Solve the linear inequality. Write the solution in set builder notation. So, -3x>15-2x, x<-15..?
  10. Algebra

    solve the following inequality. write the solution in interval notation and graph it. [2y + 4] < 10 ( the [ ] are in place of absolute values , i don't have them on my keyboard) Thanks so much!

More Similar Questions