Questions: Solve the equation for the given variable. (For no solution type DNE, and for infinite solutions select the infinity symbol.) 8x+4-2x+9=6x+13 Answer: x=

Solution Steps

To solve the equation \(8x + 4 - 2x + 9 = 6x + 13\), we need to simplify both sides of the equation and then isolate the variable \(x\).

1. Combine like terms on both sides.
2. Move all terms involving \(x\) to one side and constant terms to the other side.
3. Solve for \(x\).

First, we combine like terms on both sides of the equation: \[ 8x + 4 - 2x + 9 = 6x + 13 \] Simplifying both sides, we get: \[ (8x - 2x) + (4 + 9) = 6x + 13 \] \[ 6x + 13 = 6x + 13 \]

Next, we move all terms involving \(x\) to one side and constant terms to the other side: \[ 6x + 13 - 6x = 6x + 13 - 6x \] \[ 13 = 13 \]

The equation simplifies to \(13 = 13\), which is always true. This indicates that the original equation is an identity, meaning it holds for all values of \(x\).

Final Answer