Questions: If your answer is not an integer, 6/3 x-6=1-6/9 x x=

Solution Steps

To solve the equation \(\frac{6}{3} x - 6 = 1 - \frac{6}{9} x\), we will first simplify the fractions and then combine like terms. After that, we will isolate the variable \(x\) on one side of the equation to find its value.

We start with the equation: \[ \frac{6}{3} x - 6 = 1 - \frac{6}{9} x \] Simplifying the fractions, we have: \[ 2x - 6 = 1 - \frac{2}{3} x \]

Next, we will add \(\frac{2}{3} x\) to both sides: \[ 2x + \frac{2}{3} x - 6 = 1 \] To combine the \(x\) terms, we convert \(2x\) to a fraction: \[ \frac{6}{3} x + \frac{2}{3} x - 6 = 1 \] This simplifies to: \[ \frac{8}{3} x - 6 = 1 \]

Now, we add 6 to both sides: \[ \frac{8}{3} x = 7 \] Multiplying both sides by \(\frac{3}{8}\) gives: \[ x = \frac{21}{8} = 2.625 \]

Final Answer