Question

Solve equations by applying the distributive property to simplify both sides of the equation if needed

-3(e+1)=2(e+11)
2k+6=3(2k-14)
8(x+3)= -4(2x-2)

Answer 1

To solve the equations, apply the distributive property to simplify both sides of the equation if needed. Then, combine like terms and solve for the variable.

Step-by-step explanation:

To solve the equations, we need to apply the distributive property to simplify both sides if needed.

1. -3(e+1) = 2(e+11)
2. 2k+6 = 3(2k-14)
3. 8(x+3) = -4(2x-2)

Let's solve each equation:

1. -3(e+1) = 2(e+11)
   -3e - 3 = 2e + 22
   -3e - 2e = 25
   -5e = 25
   e = -5
2. 2k+6 = 3(2k-14)
   2k + 6 = 6k - 42
   6 + 42 = 6k - 2k
   48 = 4k
   k = 12
3. 8(x+3) = -4(2x-2)
   8x + 24 = -8x + 8
   8x + 8x = 8 - 24
   16x = -16
   x = -1

The solutions for the equations are: e = -5, k = 12, and x = -1.