Answer:
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