Question: User: 22+54x=\-20+60x
1. **State the problem:** Solve the linear equation $$22 + 54x = -20 + 60x$$.
2. **Write down the formula and rules:** To solve for $$x$$, we want to isolate $$x$$ on one side of the equation by performing the same operations on both sides.
3. **Step 1: Move all $$x$$ terms to one side and constants to the other:**
$$22 + 54x = -20 + 60x$$
Subtract $$54x$$ from both sides:
$$22 + \cancel{54x} - \cancel{54x} = -20 + 60x - 54x$$
Simplifies to:
$$22 = -20 + 6x$$
4. **Step 2: Move constants to one side:**
Add $$20$$ to both sides:
$$22 + 20 = -20 + 20 + 6x$$
Simplifies to:
$$42 = 6x$$
5. **Step 3: Solve for $$x$$ by dividing both sides by $$6$$:**
$$\frac{42}{\cancel{6}} = \frac{6x}{\cancel{6}}$$
Simplifies to:
$$7 = x$$
6. **Final answer:**
$$x = 7$$