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?

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

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step-by-step explanation: