We included **HMH Into Math Grade 7 Answer Key PDF** **Module 8 Solve Problems Using Inequalities **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 8 Answer Key Solve Problems Using Inequalities

**The Suspect is Over There!**

In your work with the Math Detective Agency, you have been asked to locate an integer suspect using witness reports given as inequalities. For example, the report x ≥ \(\frac{4}{5}\) means that the witness believes the suspect is greater than or equal to four-fifths.

Summarize each report by graphing the inequality on the number line.

A. x ≥ \(\frac{4}{5}\)

Answer:

x ≥ 0.8

Explanation:

we plot them on intervals of number line.

Numbers present on right are larger than the numbers present on left of the number line.

x ≥ \(\frac{4}{5}\)

x ≥ 0.8

B. y < 6

Answer:

Explanation:

we plot them on intervals of number line.

Numbers present on right are larger than the numbers present on left of the number line.

C. n ≤ 2.8

Answer:

Explanation:

we plot them on intervals of number line.

Numbers present on right are larger than the numbers present on left of the number line.

D. p > \(\frac{8}{5}\)

Answer:

Explanation:

when comparing numbers bigger than nine, we plot them on intervals of number line.

Numbers present on right are larger than the numbers present on left of the number line.

p > \(\frac{8}{5}\)

p > 1.6

**Turn and Talk**

If all the witness reports are correct, do you have enough information to determine which integer is the suspect? Explain.

Answer:

No

Explanation:

We still don’t have much information about the suspects as the suspect can be anywhere from

0.8 to 6.0

So we can not identify the suspect integer.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Compare Rational Numbers**

**Compare. Write < or >.**

Question 1.

-7 -3

Answer:

-7 < -3

Explanation:

Zero on number line is neither a positive number or a negative number.

-3 is closer to zero on number line.

So, -7 is less than -3.

Question 2.

0 -1

Answer:

0 > -1

Explanation:

Zero on number line is neither a positive number or a negative number.

So, zero greater than -1.

Question 3.

\(\frac{1}{3}\) –\(\frac{3}{4}\)

Answer:

\(\frac{1}{3}\) > –\(\frac{3}{4}\)

Explanation:

To compare the fractional numbers first reduce them to their standard forms,

\(\frac{1}{3}\) = 0.3

–\(\frac{3}{4}\) = -0.75

So, \(\frac{1}{3}\) is greater than \(\frac{3}{4}\)

Question 4.

-2.10 -2.19

Answer:

-2.10 > -2.19

Explanation:

To compare the negative integers on number line observe the tenth place of the given numbers as the whole numbers and ones place have same numbers.

So, -2.10 > -2.19

Question 5.

-7\(\frac{2}{5}\) 5\(\frac{1}{2}\)

Answer:

-7\(\frac{2}{5}\) < 5\(\frac{1}{2}\)

Explanation:

To compare the mixed numbers first reduce them to their standard forms,

-7\(\frac{2}{5}\) = –\(\frac{37}{5}\) = -7.4

5\(\frac{1}{2}\) = \(\frac{11}{2}\) = 5.5

So, -7\(\frac{2}{5}\) is less than 5\(\frac{1}{2}\)

Question 6.

–\(\frac{2}{5}\) -0.35

Answer:

–\(\frac{2}{5}\) < -0.35

Explanation:

Convert fractional number to their standard form,

–\(\frac{2}{5}\) = -0.4

So, –\(\frac{2}{5}\) is less than -0.35

**Interpret, Write, and Graph Inequalities**

**For each inequality, circle the values in the box that can be substituted for the variable to make the inequality true.**

Question 7.

x + 2.4 < 8.6

Answer:

Explanation:

x + 2.4 < 8.6

x < 8.6 – 2.4

x < 6.2

Question 8.

\(\frac{1}{3}\)n > \(\frac{2}{5}\)

Answer:

Explanation:

\(\frac{1}{3}\)n > \(\frac{2}{5}\)

n > \(\frac{2}{5}\) x \(\frac{3}{1}\)

n > \(\frac{6}{5}\)

**Write an inequality to represent each situation.**

Question 9.

The temperature t in a freezer must be at most -10 °F.

Answer:

temperature <= -10

Explanation:

At most means the temperature can be any value less than or equal to -10

Question 10.

A person’s weight w must be more than 110 pounds for the person to donate blood to a blood bank.

Answer:

w > 110

Explanation :

the weight should be greater than 110 pounds so we use < sign

**Graph each inequality.**

Question 11.

x < 16

Answer:

Explanation:

x < 16

all the values below 16 can be considered x

x = 15 , 14 . 13 , 12 , 11, 10 , 9 , 8 , ………

Question 12.

n > 5.2

Answer:

Explanation :

n > 5.2

All the values less than 5.2 are considered x