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

d is correct

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752