In the equation 4y + 5 - 7 = 2y + 6, what does y equal?

In the equation 4y + 5 - 7 = 2y + 6, what does y equal?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (D)

To solve the equation \(4y + 5 - 7 = 2y + 6\), begin by simplifying both sides of the equation. First, combine the constants on the left side: \[ 4y + 5 - 7 = 4y - 2 \] Now the equation reads: \[ 4y - 2 = 2y + 6 \] Next, isolate the variable \(y\) by eliminating \(2y\) from both sides: \[ 4y - 2y - 2 = 6 \] This simplifies to: \[ 2y - 2 = 6 \] To isolate the term \(2y\), add 2 to both sides: \[ 2y = 8 \] Now, divide both sides by 2 to solve for \(y\): \[ y = 4 \] The correct solution to the equation is thus \(y = 4\). This reflects mathematical principles of balancing equations and isolating variables, which are both fundamental concepts in algebra. In this case, correctly following the steps of rearranging terms and performing inverse operations leads to the determination of \(y\). The options

To solve the equation (4y + 5 - 7 = 2y + 6), begin by simplifying both sides of the equation. First, combine the constants on the left side:

[

4y + 5 - 7 = 4y - 2

]

Now the equation reads:

[

4y - 2 = 2y + 6

]

Next, isolate the variable (y) by eliminating (2y) from both sides:

[

4y - 2y - 2 = 6

]

This simplifies to:

[

2y - 2 = 6

]

To isolate the term (2y), add 2 to both sides:

[

2y = 8

]

Now, divide both sides by 2 to solve for (y):

[

y = 4

]

The correct solution to the equation is thus (y = 4). This reflects mathematical principles of balancing equations and isolating variables, which are both fundamental concepts in algebra. In this case, correctly following the steps of rearranging terms and performing inverse operations leads to the determination of (y). The options