directions: translate each expression.
1. he sum of a number and 4.\
2. he quotient of a number and -2.\
3. he product of a number and 5.\
4. he difference of a number and 7.\
5. \a number squared increased by 1\
6. hree less than twice a number\
directions: translate each equation. do not solve!
7. wice a number divided by 6 is 42.\
8. wo times the sum of number and 5 is 20\
9. \four times the difference of a number and 7 is 32\
10. \one-third of a number is 12 less than the number itself\
11. en increased by the quotient of a number and 2 is -15\
12. \one less than the product of a number and 3 is 5 more than the number itself\
directions: translate each inequality.
13. \a number less than 15\
14. \a number greater than or equal to -3\
15. \a number that is at least 90\
16. \a speed limit of 65 mph\
17. \a number that is no more than 20\
18. \a maximum number of 50\
19. \a minimum number of 10\
20. \a number no less than 25\

Question

directions: translate each expression.
1. 	he sum of a number and 4.\
2. 	he quotient of a number and -2.\
3. 	he product of a number and 5.\
4. 	he difference of a number and 7.\
5. \a number squared increased by 1\
6. 	hree less than twice a number\
directions: translate each equation. do not solve!
7. 	wice a number divided by 6 is 42.\
8. 	wo times the sum of number and 5 is 20\
9. \four times the difference of a number and 7 is 32\
10. \one-third of a number is 12 less than the number itself\
11. 	en increased by the quotient of a number and 2 is -15\
12. \one less than the product of a number and 3 is 5 more than the number itself\
directions: translate each inequality.
13. \a number less than 15\
14. \a number greater than or equal to -3\
15. \a number that is at least 90\
16. \a speed limit of 65 mph\
17. \a number that is no more than 20\
18. \a maximum number of 50\
19. \a minimum number of 10\
20. \a number no less than 25\

Accepted Answer

### 1. "the sum of a number and 4."
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Sum" means addition, so we add $ x $ and 4.
$ x + 4 $
# Answer: $ x + 4 $

### 2. "the quotient of a number and -2."
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Quotient" means division, so we divide $ x $ by -2.
$ \frac{x}{-2} $ or $ -\frac{x}{2} $
# Answer: $ \frac{x}{-2} $ (or $ -\frac{x}{2} $)

### 3. "the product of a number and 5."
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Product" means multiplication, so we multiply $ x $ by 5.
$ 5x $
# Answer: $ 5x $

### 4. "the difference of a number and 7."
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Difference" means subtraction, so we subtract 7 from $ x $.
$ x - 7 $
# Answer: $ x - 7 $

### 5. "a number squared increased by 1"
# Explanation:
## Step1: Let the number be $ x $. "Squared" means $ x^2 $.
## Step2: "Increased by" means addition, so we add 1 to $ x^2 $.
$ x^2 + 1 $
# Answer: $ x^2 + 1 $

### 6. "three less than twice a number"
# Explanation:
## Step1: Let the number be $ x $. "Twice a number" is $ 2x $.
## Step2: "Three less than" means we subtract 3 from $ 2x $.
$ 2x - 3 $
# Answer: $ 2x - 3 $

### 7. "twice a number divided by 6 is 42."
# Explanation:
## Step1: Let the number be $ x $. "Twice a number" is $ 2x $.
## Step2: "Divided by 6" gives $ \frac{2x}{6} $, and "is" means equals 42.
$ \frac{2x}{6} = 42 $
# Answer: $ \frac{2x}{6} = 42 $

### 8. "two times the sum of number and 5 is 20"
# Explanation:
## Step1: Let the number be $ x $. "Sum of a number and 5" is $ x + 5 $.
## Step2: "Two times" that sum is $ 2(x + 5) $, and "is" means equals 20.
$ 2(x + 5) = 20 $
# Answer: $ 2(x + 5) = 20 $

### 9. "four times the difference of a number and 7 is 32"
# Explanation:
## Step1: Let the number be $ x $. "Difference of a number and 7" is $ x - 7 $.
## Step2: "Four times" that difference is $ 4(x - 7) $, and "is" means equals 32.
$ 4(x - 7) = 32 $
# Answer: $ 4(x - 7) = 32 $

### 10. "one - third of a number is 12 less than the number itself"
# Explanation:
## Step1: Let the number be $ x $. "One - third of a number" is $ \frac{1}{3}x $.
## Step2: "12 less than the number itself" is $ x - 12 $, and "is" means they are equal.
$ \frac{1}{3}x = x - 12 $
# Answer: $ \frac{1}{3}x = x - 12 $

### 11. "ten increased by the quotient of a number and 2 is - 15"
# Explanation:
## Step1: Let the number be $ x $. "Quotient of a number and 2" is $ \frac{x}{2} $.
## Step2: "Ten increased by" that quotient is $ 10+\frac{x}{2} $, and "is" means equals - 15.
$ 10+\frac{x}{2}=-15 $
# Answer: $ 10 + \frac{x}{2} = -15 $

### 12. "one less than the product of a number and 3 is 5 more than the number itself"
# Explanation:
## Step1: Let the number be $ x $. "Product of a number and 3" is $ 3x $. "One less than" that product is $ 3x - 1 $.
## Step2: "5 more than the number itself" is $ x + 5 $, and "is" means they are equal.
$ 3x - 1 = x + 5 $
# Answer: $ 3x - 1 = x + 5 $

### 13. "a number less than 15"
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Less than" means $ x < 15 $
$ x < 15 $
# Answer: $ x < 15 $

### 14. "a number greater than or equal to - 3"
# Explanation:
## Step1: Let the number be $ x $.
## Step2: "Greater than or equal to" means $ x\geq - 3 $
$ x\geq - 3 $
# Answer: $ x \geq -3 $

### 15. "a number that is at least 90"
# Explanation:
## Step1: Let the number be $ x $. "At least" means greater than or equal to.
## Step2: So $ x\geq90 $
$ x\geq90 $
# Answer: $ x \geq 90 $

### 16. "a speed limit of 65 mph"
# Explanation:
## Step1: Let the speed be $ x $ (in mph).
## Step2: A speed limit of 65 mph means the speed is less than or equal to 65, so $ x\leq65 $
$ x \leq 65 $
# Answer: $ x \leq 65 $ (where $ x $ is speed in mph)

### 17. "a number that is no more than 20"
# Explanation:
## Step1: Let the number be $ x $. "No more than" means less than or equal to.
## Step2: So $ x\leq20 $
$ x\leq20 $
# Answer: $ x \leq 20 $

### 18. "a maximum number of 50"
# Explanation:
## Step1: Let the number be $ x $. "Maximum" means the number is less than or equal to 50.
## Step2: So $ x\leq50 $
$ x\leq50 $
# Answer: $ x \leq 50 $

### 19. "a minimum number of 10"
# Explanation:
## Step1: Let the number be $ x $. "Minimum" means the number is greater than or equal to 10.
## Step2: So $ x\geq10 $
$ x\geq10 $
# Answer: $ x \geq 10 $

### 20. "a number no less than 25"
# Explanation:
## Step1: Let the number be $ x $. "No less than" means greater than or equal to.
## Step2: So $ x\geq25 $
$ x\geq25 $
# Answer: $ x \geq 25 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. "the sum of a number and 4."

Step1: Let the number be \( x \).

Step2: "Sum" means addition, so we add \( x \) and 4.

Step1: Let the number be \( x \).

Step2: "Quotient" means division, so we divide \( x \) by -2.

Step1: Let the number be \( x \).

Step2: "Product" means multiplication, so we multiply \( x \) by 5.

Answer:

2. "the quotient of a number and -2."