Select the values that make the inequality 6, z, is less than, 126z<12 true. Then write an equivalent inequality, in terms of zz.

(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2

-8 -3 -1
1 2 3
5 7 12
Equivalent Inequality:

1 answer

To solve the inequality 6z<126z<12, let's break it down into two parts.

  1. First Inequality: 6z<126z

    We can simplify this by subtracting 6z from both sides:

    0<120z

    Dividing both sides by 120 (which is positive):

    0<zorz>0

  2. Second Inequality: 126z<12

    We can simplify this by dividing both sides by 126:

    z<12126

    Simplifying 12126:

    12126=221

    Thus, the second part gives us:

    z<221

Now, combining both results, we can write the compound inequality as:

0<z<221

In interval notation, this corresponds to the interval (0,221).

Select the Values

From the provided options, we check which values fall within the interval (0,221). Since 2210.0952, we see that the only number in the provided options falling within this interval is 1.

Equivalent Inequality

The equivalent inequality in terms of z can therefore be written as:

0<z<221

Answers

  1. Selected value: 1
  2. Equivalent Inequality: 0<z<221