Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

a number line from negative 5 to 5 in increments of 1. an open circle is at 3 and a bold line starts at 3 and is pointing to the left.
a number line from negative 5 to 5 in increments of 1. an open circle is at 3 and a bold line starts at 3 and is pointing to the right.
a number line from negative 5 to 5 in increments of 1. an open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
a number line from negative 5 to 5 in increments of 1. an open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

  A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Step-by-step explanation:

We can start by dividing the inequality by 3 to get ...

  8 -4x < 2(x -5)

And we can divide by 2 to simplify further to ...

  4 -2x < x -5

Now, we can add 2x+5, which gives ...

  9 < 3x

and then divide by 3 again:

  3 < x

This is graphed on a number line as described above.

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since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: