1. **State the problem:** Find the value of $x$ in the arithmetic sequence with first three terms: 6, $x$, -4. 2. **Recall the formula for an arithmetic sequence:** The difference between consecutive terms is constant, called the common difference $d$. 3. **Set up the equation:** Since the sequence is arithmetic, the difference between the second and first term equals the difference between the third and second term: $$x - 6 = -4 - x$$ 4. **Solve for $x$:** $$x - 6 = -4 - x$$ Add $x$ to both sides: $$x + x - 6 = -4$$ $$2x - 6 = -4$$ Add 6 to both sides: $$2x = -4 + 6$$ $$2x = 2$$ Divide both sides by 2: $$\cancel{2}x = \cancel{2}1$$ $$x = 1$$ 5. **Answer:** The value of $x$ is $1$.