1. **State the problem:** Solve the linear equation $$17.95x + 24 = 18.95x + 18$$ to find the value of $x$ where the two expressions are equal. 2. **Write the equation:** $$17.95x + 24 = 18.95x + 18$$ 3. **Isolate the variable terms on one side:** Subtract $17.95x$ from both sides: $$\cancel{17.95x} + 24 = (18.95x - 17.95x) + 18$$ which simplifies to $$24 = 1.00x + 18$$ 4. **Isolate $x$:** Subtract 18 from both sides: $$24 - 18 = 1.00x + \cancel{18} - 18$$ which simplifies to $$6 = 1.00x$$ 5. **Solve for $x$:** Divide both sides by 1.00: $$\frac{6}{\cancel{1.00}} = \frac{1.00x}{\cancel{1.00}}$$ which simplifies to $$x = 6$$ **Final answer:** $$x = 6$$ This means the cost is the same when buying 6 pairs of pants.