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

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 ≥ $$\frac{4}{5}$$

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

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

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 > $$\frac{8}{5}$$

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.
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.

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
-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
0 > -1
Explanation:
Zero on number line is neither a positive number or a negative number.
So, zero greater than -1.

Question 3.
$$\frac{1}{3}$$ –$$\frac{3}{4}$$
$$\frac{1}{3}$$ > –$$\frac{3}{4}$$
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
-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$$\frac{1}{2}$$
-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
–$$\frac{2}{5}$$ < -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

Explanation:
x + 2.4 < 8.6
x < 8.6 – 2.4
x < 6.2

Question 8.
$$\frac{1}{3}$$n > $$\frac{2}{5}$$

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.
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.
w > 110

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

Graph each inequality.

Question 11.
x < 16

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