1. how many solutions does - 3x + 32 - 7x = - 2 (5x + 10) have?

a. infinitely

b. one

c. none

2. how many solutions does 3 (x - 14) + 1 = - 4x + 5 have?

1.) none

2.) 46/7

Solve each equation for x

1.

-3x + 32 - 7x = - 2 (5x + 10)

-3x+32-7x = - 2*5x + -2*10 Distribute the - 2 on the right

-3x+32-7x = - 10x - 20

(-3x-7x) + 32 = - 10x-20 Combine like terms

-10x+32=-10x-20

-10x+10x + 32 = - 10x+10x - 20 Add 10x to both sides

32=-20

Since this statement is not true, this equation has no solutions.

2.

3 (x - 14) + 1 = - 4x + 5

3*x + 3*-14 + 1 = -4x+5 Distribute the 3 on the left

3x-42+1 = - 4x+5

3x-41 = - 4x+5 Combine like terms

3x+4x-41 = - 4x+4x+5 Add 4x to both sides

7x-41=5

7x-41+41=5+41 Add 41 to both sides

7x=46

7x/7=46/7 Divide both sides by 7

x=46/7

This equation has one solution, 46/7