Question

1. 3 added to x is 5
2. one - fourth of x is 21.
3. six times a number is 48.
4. twice a number is 8.
5. the sum of 4x and 3 is 11.
6. a number increased by 6 is 21.
7. the product of a number and 7 is 42.
8. the sum of - 5 and a number is 23.
9. a number decreased by 9 is 6.
10. a number subtracted from 4 is 32.

a. 2x = 8
b. x + 6 = 21
c. 7x = 42
d. - 8 = 2x
e. 4 - x = 32
f. - 5 + x = 23
g. 1/4x = 21
h. 4x + 3 = 11
i. x + 3 = 5
j. x - 9 = 6
k. 6x = 48
l. x - 9 = - 6

b. match each statement to its equation

Explanation:

To solve this matching problem, we analyze each statement and translate it into an algebraic equation:

1. "3 added to \( x \) is 5"

Translation: \( x + 3 = 5 \) → Matches i

2. "One - fourth of \( x \) is 21"

Translation: \( \frac{1}{4}x = 21 \) → Matches g

3. "Six times a number is 48"

Let the number be \( x \). Translation: \( 6x = 48 \) → Matches k

4. "Twice a number is 8"

Let the number be \( x \). Translation: \( 2x = 8 \) → Matches a

5. "The sum of \( 4x \) and 3 is 11"

Translation: \( 4x + 3 = 11 \) → Matches h

6. "A number increased by 6 is 21"

Let the number be \( x \). Translation: \( x + 6 = 21 \) → Matches b

7. "The product of a number and 7 is 42"

Let the number be \( x \). Translation: \( 7x = 42 \) → Matches c

8. "The sum of - 5 and a number is 23"

Let the number be \( x \). Translation: \( - 5 + x = 23 \) → Matches f

9. "A number decreased by 9 is 6"

Let the number be \( x \). Translation: \( x - 9 = 6 \) → Matches j

10. "A number subtracted from 4 is 32"

Translation: \( 4 - x = 32 \) → Matches e

Final Matches:

1 - i
2 - g
3 - k
4 - a
5 - h
6 - b
7 - c
8 - f
9 - j
10 - e

Answer:

To solve this matching problem, we analyze each statement and translate it into an algebraic equation:

1. "3 added to \( x \) is 5"

Translation: \( x + 3 = 5 \) → Matches i

2. "One - fourth of \( x \) is 21"

Translation: \( \frac{1}{4}x = 21 \) → Matches g

3. "Six times a number is 48"

Let the number be \( x \). Translation: \( 6x = 48 \) → Matches k

4. "Twice a number is 8"

Let the number be \( x \). Translation: \( 2x = 8 \) → Matches a

5. "The sum of \( 4x \) and 3 is 11"

Translation: \( 4x + 3 = 11 \) → Matches h

6. "A number increased by 6 is 21"

Let the number be \( x \). Translation: \( x + 6 = 21 \) → Matches b

7. "The product of a number and 7 is 42"

Let the number be \( x \). Translation: \( 7x = 42 \) → Matches c

8. "The sum of - 5 and a number is 23"

Let the number be \( x \). Translation: \( - 5 + x = 23 \) → Matches f

9. "A number decreased by 9 is 6"

Let the number be \( x \). Translation: \( x - 9 = 6 \) → Matches j

10. "A number subtracted from 4 is 32"

Translation: \( 4 - x = 32 \) → Matches e

Final Matches:

1 - i
2 - g
3 - k
4 - a
5 - h
6 - b
7 - c
8 - f
9 - j
10 - e