How do you solve #4[2( - 5x + y ) - y]= 10( y - 4x )#?

Question

Kennedy Adams · Accepted Answer

# y = 0#

# 4 [ 2( -5x +y) - y ] = 10 (y - 4x)#

Step 1: Open the brackets. First the innermost on left-hand-side and the one on right- hand- side

# 4 [ - 10x + 2y - y ] = 10y - 40x#

Step 2: Simplify

# 4 [ -10x + y] = 10y -40x #

Step 3: Open the square bracket:

# -40x + 4y = 10y - 40x #

Step 4: Bring the terms with variable #x# on left- hand side of the equation and take the terms with #y# variable on right-hand-side. Or vice versa.

Transposition

# - 40x + 40x = 10y - 4y #

Step 5: Solve # 0x = 6y# or # 6y = 0x# i.e. #y = 0#

Cross check by substituting the obtained value of #y# in the given equation:

# 4 [ 2( -5x +y) - y ] = 10 (y - 4x)#

# 4 [ 2 (-5x + 0)- 0 ] = 10 (0 - 4x)#

#4 [ -10x] = 10 (-4x)#

# - 40 x = - 40x #

Left-hand-side = right-hand-side

Savannah Anderson · Answer

undefined To solve the equation $4[2(-5x + y) - y] = 10(y - 4x)$, follow these steps:

1. Distribute the terms inside the brackets:
   $4[2(-5x) + 2y - y] = 10y - 40x$

2. Simplify inside the brackets:
   $4[-10x + 2y - y] = 10y - 40x$

3. Combine like terms inside the brackets:
   $4[-10x + y] = 10y - 40x$

4. Distribute the 4 outside the brackets:
   $-40x + 4y = 10y - 40x$

5. Rearrange the terms to isolate the variable:
   $4y - 10y = -40x + 40x$

6. Combine like terms:
   $-6y = 0$

7. Solve for $y$:
   $y = 0$

8. Substitute the value of $y$ into one of the original equations to find $x$.

Thus, the solution to the equation is $x$ can be any real number, and $y = 0$.

Abigail Allen · Answer

undefined To solve the equation 4[2( - 5x + y ) - y]= 10( y - 4x ), follow these steps:

1. Distribute the 4 on the left side of the equation:
   4 * 2 * (-5x + y) - 4 * y = 10(y - 4x)

2. Simplify each term:
   8 * (-5x + y) - 4y = 10y - 40x

3. Distribute the 8 on the left side of the equation:
   8 * (-5x) + 8y - 4y = 10y - 40x

4. Simplify each term:
   -40x + 8y - 4y = 10y - 40x

5. Combine like terms:
   -40x + 4y = 10y - 40x

6. Add 40x to both sides of the equation to isolate the y terms:
   4y = 10y

7. Subtract 10y from both sides:
   4y - 10y = 0

8. Combine like terms:
   -6y = 0

9. Divide both sides by -6 to solve for y:
   y = 0

10. Substitute y = 0 back into the original equation to solve for x:
    4[2(-5x + 0) - 0] = 10(0 - 4x)

11. Simplify each side of the equation:
    4(-10x) = -40x

12. Distribute the 4:
    -40x = -40x

Since both sides of the equation are equal, this equation is true for all values of x when y = 0. Therefore, the solution is (x, y) = (any real number, 0).