Question

1. higher order thinking in the equation $10 + 4y = -4y + 2$, the variable $y$ represents the same value. is $y = 1$, $0$, $-1$, or $-2$ the solution of this equation? explain.

Explanation:

Step1: Solve the equation for y

We start with the equation \(10 + 4y=-4y + 2\). First, we add \(4y\) to both sides to get all the \(y\) terms on one side.
\(10 + 4y+4y=-4y + 2+4y\)
Simplifying both sides, we have \(10 + 8y=2\).
Then, we subtract 10 from both sides:
\(10 + 8y-10=2 - 10\)
Which simplifies to \(8y=-8\).
Finally, we divide both sides by 8:
\(y=\frac{-8}{8}=-1\)

Step2: Verify by substitution (optional but good practice)

We can also check each value:

• For \(y = 1\): Left side \(10+4(1)=14\), Right side \(-4(1)+2=-2\). \(14

eq - 2\), so not a solution.

• For \(y = 0\): Left side \(10+4(0)=10\), Right side \(-4(0)+2 = 2\). \(10

eq2\), so not a solution.

• For \(y=-1\): Left side \(10 + 4(-1)=10-4 = 6\), Right side \(-4(-1)+2=4 + 2=6\). Both sides are equal, so it is a solution.
• For \(y=-2\): Left side \(10+4(-2)=10 - 8=2\), Right side \(-4(-2)+2=8 + 2 = 10\). \(2

eq10\), so not a solution.

Answer:

\(y=-1\) is the solution of the equation \(10 + 4y=-4y + 2\).