2. Solve each given location and show your work. Tell whether each equation has one solution, an infinite number of solutions, or no solutions. Explain your answers. (a) 4x + 2 (x - 1) = 10 + 2x (b) 30 - x = 10 - (6 + 10) (c) 8x = 4x + 4x + 10 (x-x) Answers:

a one solutions x=3

b one solution x=36

c infinite solutions

Step-by-step explanation:

(a) 4x + 2 (x - 1) = 10 + 2x

Distribute

4x+2x-2 = 10+2x

Combine like terms

6x-2 = 10+2x

Subtract 2x from each side

6x-2x-2 = 10+2x-2x

4x-2 = 10

Add 2 to each side

4x-2+2 = 10+2

4x=12

Divide by 4

4x/4 = 12/4

x=3

There is one solution

(b) 30 - x = 10 - (6 + 10)

Distribute the minus sign

30-x = 10-6-10

30-x=-6

Subtract 30 from each side

30-x-30 = - 6-30

-x = - 36

Multiply by - 1

x = 36

(c) 8x = 4x + 4x + 10 (x-x)

Parentheses first

8x = 4x+4x+10 (0)

8x=4x+4x

Combine like terms

8x=8x

Subtract 8x from each side

8x-8x=8x-8x

0=0

This is always a true statement

x = all real numbers

infinite solutions