A few Math questions?

Question

1) Solve for h. v = (pi)(r^2)(h) 

2) True or False? The first step in solving |2x - 8| + 4 = 10 is to subtract 4 from each side of the equation.

3) Solve for n. (3(n - 19)) / (5) = 0 

4) Solve for y. 5x - y = 3 

5) Solve for n. (2 / 7)n - 5 = 5

Update : Theres five more, if someone doesn't mind. 

6) Solve for n. -(14n - 8) = - (9n - 8) - 5n 

7) Solve the equation for c and show your work. -2(c + 19) = -52 

8) Solve for n. |3n - 12| = 6 

9) Solve for n. 3n - 5 = 8n - 5 

10) Solve the equation for n and show your work. -3n + 48 = 0

Answer 1

1) The equation

divide each side by .

Solution

2) The absolute equation is | 2x - 8| + 4 = 10

To solve the absolute equations , absolute-value expression by itself on one side of the "equals" sign, with everything else on the other side.

| 2x - 8| + 4 = 10

Subtract 4 from each side.

| 2x - 8| + 4 - 4 = 10 - 4

| 2x - 8| = 6

Apply the formula | x | = a then x = a or x = - a

2x - 8 = 6 or 2x - 8 = - 6

2x = 14 or 2x = 2

Solutions are x = 7 or x = 1.

You are correct. first step is true.

Answer 2

3) The equation (3(n - 19))/5 = 0

Multiply each side by 5.

[(3(n - 19))/5]5 = 5(0)

3(n - 19) = 0

Apply distributive property a( b + c) = ab + ac.

3(n) + 3(-19) = 0

3n - 57 = 0

3n = 57

n = 57/3

Solution n = 19.

Answer 3

4)

The equation 5x - y = 3

Subtract 5x from each side.

- y = - 5x + 3

Multiply each side by negative one.

y = 5x - 3.

Answer 4

5) The equation (2/7)n - 5 = 5

Add 5 to each side.

(2/7)n - 5 + 5 = 5 + 5

Apply additive inverse property: – a + a = 0

(2/7)n = 10

Multiply each side by (7/2).

(2/7)(7/2) n = 10(7/2)

n = 70/2

Solution n = 35.

Answer 5

6) The equation - (14n - 8) = - (9n - 8) - 5n

- 14n + 8 = - 9n + 8 - 5n

- 14n + 8 = - 14n + 8

Bring all terms to left side.

- 14n + 14n + 8 - 8 = 0

0 = 0.

Answer 6

7)The equation  - 2(c + 19) = - 52

Apply distributive property a( b + c) = ab + ac.

(-2)(c) + (-2)(19) = - 52

-2c - 38 = - 52

Add 38 to each side.

- 2c - 38 + 38 = - 52 + 38

- 2c = -14

Divide each side by negative 2.

(-2c)/(-2) = (-14)/(-2)

c = 7

Solution c =  7.

Answer 7

8) The absolute equation | 3n - 12| = 6

Apply the formula | x |= a is equivalent to x = a or x = - a

Case 1 : 3n - 12 = 6

Add 12 to each side.

3n - 12 + 12 = 6 + 12

3n = 18

Divide each side by 3.

3n/3 = 18/3

n = 6

Case 2: 3n - 12 = - 6

Add 12 to each side.

3n - 12 + 12 = - 6 + 12

3n = 6

Divide each side by 3.

3n/3 = 6/3

n = 2

Solution: n = 6 , 2.

Answer 8

9) The equation 3n - 5 = 8n - 5

Add 5 to each side.

3n - 5 + 5 = 8n - 5 + 5

3n = 8n

Subtract 3n - 8n = 0

- 5n = 0

Divide each side by negative 5.

(- 5n)/(- 5) = 0/(- 5)

Solution n = 0.

Answer 9

10) The equation - 3n + 48 = 0

Subtract 48 from each side.

- 3n + 48 - 48 = 0 - 48

- 3n = - 48

Divide each side by negative 3.

(- 3n)/(- 3) = (- 48)/(- 3)

Solution n = 16.