Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 13 Quiz Answer Key.
Texas Go Math Grade 6 Module 13 Quiz Answer Key
Texas Go Math Grade 6 Module 13 Ready to Go On? Answer Key
13.1 Writing Inequalities
Write an inequality to represent each situation, then graph the solutions.
Question 1.
There are fewer than 8 gallons of gas in the tank. __________________
Answer:
Draw a solid circle at 8 to show that 8 is not a solution.
Shade the number line to the left of 8 to show that numbers less than 8 are solutions.
Check your answer.
Substitute 7 for g.
7 < 8; 7 is less than 8, so 7 is a solution
Graph the solution on a number line.
Question 2.
There are at least 3 pieces of gum left in the pack. __________________
Answer:
Because here we have “at least 3″, the required inequality would be graphed on the following picture.
The inequality which describes given situation would be x ≥ 3.
Question 3.
The valley was at least 4 feet below sea level. ______________________
Answer:
Because here we have “at least 4″, the required inequality would be graphed on the following picture.
The inequality which describes given situation would be x ≥ 4.
13.2 Addition and Subtraction Inequalities
Solve each inequality. Graph the solution.
Question 4.
c – 28 > -32
Answer:
We will add 28 to both sides in order to solve this inequality and get:
c > -4
Now, we will graph the solution:
Now we will check our solution substituting some value from the set of solutions we got in originaL inequation. We will substitute 0 for c and get:
0 – 28 > -32
-28 > -32
So, the inequality is true.
c <> -4
Question 5.
v + 17 ≤ 20.
Answer:
In order to solve given inequality, we need to subtract 17 from both sides and get:
v ≤ 3
Now, we will graph the solution:
Question 6.
Today’s high temperature of 80°F is at least 16° warmer than yesterday’s high temperature. What was yesterday’s high temperature?
Answer:
Let x represent yesterday’s high temperature. According to all informations, we get the following inequality:
80 – x ≥ 16
We need to subtract 80 from both sides and get:
-x ≥ -64
Next step is to multiply both sides by -1. -1 is negative number, so, we need to reverse the inequality symbol for the statement to still be true.
(-x) (-1) ≤ (-64) (-1)
x ≤ 64
So, yesterday’s high temperature was at most 64°F.
13.3, 13.4 Multiplication and Division inequalities
Solve each inequality. Graph the solution.
Question 7.
7f ≤ 35
Answer:
First step is to divide both sides by 7.
\(\frac{7f}{7}\) ≤ \(\frac{35}{7}\)
f ≤ 5
Now, we will graph the solution:
Now we will check the solution by substituting a soLution from the shaded part of the graph into the original inequality.
We will substitute 2 for f and get:
7 ∙ 2 ≤ 35
14 ≤ 35
So, the inequality is true.
f ≤ 5
Question 8.
\(\frac{a}{2}\) < 4
Answer:
First step is to multiply by 2.
2(\(\frac{a}{2}\)) < 4(2)
a < 8
Now, we will graph the solution:
Now, we will check the solution by substituting a solution from the shaded part of the graph into the original inequality. We will substitute 4 for a and get:
\(\frac{4}{2}\) < 4
2 < 4
So, the inequality is true.
a < 8
Question 9.
-25g ≥ 150
Answer:
First step is to divide both sides by -25. -25 is negative number, so we need to reverse the inequality symbol for the statement to still be true.
\(\frac{-25g}{-25}\) ≤ \(\frac{150}{-25}\)
g ≤ -6
Now, we will graph the solution:
Now we will check the solution by substituting a solution from the shaded part of the graph into the original inequality.
We will substitute -8 for g and get:
-25(-8) ≥ 150
200 ≥ 150
So, the inequality is true.
g ≤ -6
Question 10.
\(\frac{k}{-3}\) < 3
Answer:
First step is to multiply by -3. -3 is negative number, so we need to reverse the inequality symbol for the statement to still be true.
\(\frac{k}{-3}\)(-3) > 3(-3)
k > -9
Now, we will graph the solution:
Now we will check the solution by substituting a solution from the shaded part of the graph into the original inequality.
So, we will substitute 0 for k and get:
\(\frac{0}{-3}\) < 3
0 < 3 So, the inequality is true. k > -9
Texas Go Math Grade 6 Module 13 Mixed Review Texas Test Prep Answer Key
Selected Response
Question 1.
Em saves at least 20% of what she earns each week. If she earns $140 each week for 4 weeks, which inequality describes the total amount she saves?
(A) t > 112
(B) t ≥ 112
(C) t < 28 (D) t ≤ 28
Answer:
(D) t ≤ 28
Explanation:
First we will calculate how much is 20% of 140. So we will multiply 140 by \(\frac{20}{100}\) = \(\frac{1}{5}\).
140 x \(\frac{1}{5}\) = \(\frac{140 \times 1}{1 \times 5}\) = 28
So, if t represent Em’s savings, the inequality which describes given situation is: t ≤ 28
Question 2.
Which number line represents the inequality r > 6?
Answer:
(B)
Explanation:
This inequality represents numbers on the right side of 6 and because there is symbol >, the circle at 6 is not full. So, conclusion is that number line which represents the inequality r > 6 is B.
Question 3.
For which inequality below is z = 3 a solution?
(A) z + 5 ≥ 9
(B) z + 5 > 9
(C) z + 5 ≤ 8
(D) z + 5 < 8
Answer:
(C) z + 5 ≤ 8
Explanation:
Solution of inequality at C is the following:
z ≤ 3
This solution includes 3, so, for this inequality, z = 3 is a solution.
Question 4.
What is the solution to the inequality -6x < -18?
(A) x > 3
(B) x < 3
(C) x ≥ 3
(D) x ≤ 3
Answer:
(A) x > 3
Explanation:
In order to solve this inequality, we need to divide both sides by -6. -6 is negative number, so, we need to reverse the inequality symbol for the statement to still be true.
\(\frac{-6x}{-6}\) > \(\frac{-18}{-6}\)
x > 3
Question 5.
The number line below represents the solution to which inequality?
(A) \(\frac{m}{4}\) > 2.2
(B) 2m < 17.6 (C) \(\frac{m}{3}\) > 2.5
(D) 5m > 40
Answer:
(A) \(\frac{m}{4}\) > 2.2
Explanation:
On given number line there are numbers right from 8.8 and 9 is not included. That is actually m > 8.8.
We can notice that this is soLution of inequality at A.
4(\(\frac{m}{4}\)) > (2.2) (4)
m > 8.8
Question 6.
Which number line shows the solution to w – 2 ≤ 8?
Answer:
(B)
Explanation:
In order to solve given inequality, we need to add 2 to both sides:
w ≤ 10
Solution we got appropriate to B.
Gridded Response
Question 7.
Hank needs to save at least $150 to ride the bus to his grandparent’s home, If he saves $12 a week, what is the least number of weeks he needs to save?
Answer:
Let x represent the number of weeks which are needed to Hank to save required money. Using all information in this task, we got the following inequality:
12x ≥ 150
In order to soLve it, we need to divide both sides by 12.
\(\frac{12x}{12}\) ≥ \(\frac{150}{12}\)
x ≥ 12.5
So, Hank will need at least 12.5 weeks to save required money.