Need some help with number word problems, tysm if you do :)

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Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

A.

4+3=7

12-6≠21 (incorrect)

B.

7+3=10

28-3≠30 (incorrect)

C.

13+3=16

52-4=48 (correct)

D.

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

A.

13+4=17

65+3=68 (correct)

B.

-23+4= -19

-115+3≠ -76 (incorrect)

C.

17+4=21

85+3≠84 (incorrect)

D.

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

A.

5+18=23

18-15=3 (correct)

B.

8+15=23

15-24≠3 (incorrect)

C.

-13+36=23

36+39≠3 (incorrect)

D.

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

A.

8+18=26

18-16=2 (correct)

B.

9+17=26

17-18≠2 (incorrect)

C.

7+19=26

19-14≠2 (incorrect)

D.

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

you ignore the remainder, therefore the answer is y = x+2

step-by-step explanation:

you have to divide the denominator by the numerator. you can use synthetic division or long division.

[-5] .     1 .     7 .     11

x + 2 + 1/x+5