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=

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=

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

Solution

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 $x$.

Combine like terms on both sides.
Move all terms involving $x$ to one side and constant terms to the other side.
Solve for $x$.

Step 1: Combine Like Terms

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

Step 2: Isolate the Variable

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

Step 3: Analyze the Result

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 $x$.