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

Question

(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:

Answer 1

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):

   $$0<z\text{or}z>0$$

2. Second Inequality: $126z<12$

   We can simplify this by dividing both sides by $126$:

   $$z<\frac{12}{126}$$

   Simplifying $\frac{12}{126}$:

   $$\frac{12}{126}=\frac{2}{21}$$

   Thus, the second part gives us:

   $$z<\frac{2}{21}$$

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

$$0<z<\frac{2}{21}$$

In interval notation, this corresponds to the interval $(0,\frac{2}{21})$.

Select the Values

From the provided options, we check which values fall within the interval $(0,\frac{2}{21})$. Since $\frac{2}{21}\approx 0.0952$, 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:

$$0<z<\frac{2}{21}$$

Answers

1. Selected value: $1$
2. Equivalent Inequality: $0<z<\frac{2}{21}$