Solving for y in an Equation: -2(-4+y)-y=0

Question

Solve for y:

2(4+y)y=0 -2(-4+y)-y=0

Video Solution

Solution Steps

00:00 Solve
00:03 Open parentheses properly, multiply by each factor
00:14 Collect terms
00:21 Arrange the equation so that only the unknown Y is on one side
00:28 Isolate Y
00:36 Decompose the fraction into a whole number and remainder
00:47 Convert fraction to whole number
00:55 And this is the solution to the question

Step-by-Step Solution

To solve the equation 2(4+y)y=0-2(-4 + y) - y = 0, we will follow these steps:

  • Step 1: Distribute 2 -2 inside the parenthesis.
  • Step 2: Simplify and combine like terms.
  • Step 3: Solve the equation for yy.

Let's proceed with the solution:

Step 1: Distribute 2-2 in the expression 2(4+y)-2(-4 + y). This will transform the expression as follows:

2(4+y)=2×4+(2)×y=82y-2(-4 + y) = -2 \times -4 + (-2) \times y = 8 - 2y.

After distributing, the equation becomes:

82yy=08 - 2y - y = 0.

Step 2: Combine like terms. Notice that 2yy-2y - y is equivalent to 3y-3y:

83y=08 - 3y = 0.

Step 3: Solve for yy. First, isolate the term with yy by subtracting 8 from both sides:

3y=8-3y = -8.

Next, divide both sides by 3-3 to find yy:

y=83=83y = \frac{-8}{-3} = \frac{8}{3}.

Thus, the solution for yy is 83\frac{8}{3}, which can be written as a mixed number:

y=223y = 2\frac{2}{3}.

Therefore, the solution to the problem is y=223y = 2\frac{2}{3}.

Answer

y=223 y=2\frac{2}{3}