Question

Solve the equations:

-50 = -2(a + 3)
4(x - 2) = 2(x - 4) + 2x
5(y - 2) - 2 = 2(y + 1) - 5
-4(p + 1) = 2(8 - 2p)

Answer 1

To solve the equations, isolate the variables step by step. The values of 'a' and 'y' can be determined, 'x' can be any value, and there is no solution for 'p'.

Step-by-step explanation:

To solve the given equations, we will simplify and isolate the variables one by one.

1. Solve for a:
   -50 = -2(a + 3)
   Divide both sides by -2: 25 = a + 3
   Subtract 3 from both sides: 22 = a
2. Solve for x:
   4(x - 2) = 2(x - 4) + 2x
   Distribute on both sides: 4x - 8 = 2x - 8 + 2x
   Combine like terms: 4x - 8 = 4x - 8
   Subtract 4x from both sides: -8 = -8
   Since the equation simplifies to a true statement, x can be any value.
3. Solve for y:
   5(y - 2) - 2 = 2(y + 1) - 5
   Distribute on both sides: 5y - 10 - 2 = 2y + 2 - 5
   Combine like terms: 5y - 12 = 2y - 3
   Subtract 2y from both sides: 3y - 12 = -3
   Add 12 to both sides: 3y = 9
   Divide both sides by 3: y = 3
4. Solve for p:
   -4(p + 1) = 2(8 - 2p)
   Distribute on both sides: -4p - 4 = 16 - 4p
   Add 4p to both sides: -4p + 4p - 4 = 16
   Combine like terms: -4 = 16
   Since the equation simplifies to a false statement, there is no solution for p.