vocabulary
choose the correct term from the vocabulary box.
1. a mathematical sentence that shows the relationship between quantities that are not equal
2. a mathematical sentence that shows that two expressions are equivalent
3. 3 is the ______ of the equation $b + 2 = 5$
4. 9 is a ______ $x

Question

vocabulary
choose the correct term from the vocabulary box.
1. a mathematical sentence that shows the relationship between quantities that are not equal
2. a mathematical sentence that shows that two expressions are equivalent
3. 3 is the ______ of the equation $b + 2 = 5$
4. 9 is a ______ $x < 10$
vocabulary
equation
solution
inequality
solution of the inequality

concepts and skills
5. use tools a komodo dragon can grow to be 120 inches long. one komodo dragon is 92 inches long. write and solve an equation to find the number of inches $x$ the komodo dragon still needs to grow to be 120 inches long. state what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

6. dakota has been assigned 80 math problems that are due in 5 days.
a. write an equation to determine how many problems she should do each day if she wants to do the same number each day. choose any letter for the variable and explain what it represents.

b. solve the equation. how many problems should dakota do each day?

Accepted Answer

### Vocabulary
1.
# Brief Explanations:
An inequality is a mathematical sentence that shows the relationship between quantities that are not equal.
# Answer:
inequality

2.
# Brief Explanations:
An equation is a mathematical sentence that shows that two expressions are equivalent.
# Answer:
equation

3.
# Brief Explanations:
For the equation $ b + 2 = 5 $, solving for $ b $ gives $ b=5 - 2=3 $, so 3 is the solution of the equation.
# Answer:
solution

4.
# Brief Explanations:
For the inequality $ x<10 $, when $ x = 5 $, $ 5<10 $ is true, so 5 is a solution of the inequality.
# Answer:
solution of the inequality

### Concepts and Skills
5.
# Explanation:
## Step1: Define the variable and set up the equation
Let $ x $ be the number of inches the Komodo dragon still needs to grow. The current length is 92 inches, and the target length is 120 inches. So the equation is $ 92 + x=120 $.
## Step2: Solve the equation
Subtract 92 from both sides of the equation: $ x = 120 - 92 $
## Step3: Calculate the value of $ x $
$ x=28 $
# Answer:
The equation is $ 92 + x = 120 $, and the solution is $ x = 28 $. We use the strategy of setting up an equation based on the relationship between the current length, the growth needed, and the target length. The tool used is basic algebraic manipulation (subtraction property of equality) to solve for $ x $.

6.
### Part A
# Brief Explanations:
Let $ x $ be the number of problems Dakota should do each day. She has 5 days to complete 80 problems, and if she does $ x $ problems each day, the total number of problems done in 5 days is $ 5x $. So the equation is $ 5x = 80 $, where $ x $ represents the number of problems per day.
# Answer:
The equation is $ 5x = 80 $, where $ x $ is the number of problems Dakota should do each day.

### Part B
# Explanation:
## Step1: Start with the equation $ 5x = 80 $
## Step2: Solve for $ x $ by dividing both sides by 5
$ x=\frac{80}{5} $
## Step3: Calculate the value of $ x $
$ x = 16 $
# Answer:
Dakota should do 16 problems each day.

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