1. **State the problem:** We want to find the distance $x$ (in kilometers) where the rental costs from company A and company B are equal. 2. **Define variables and write the cost functions:** - Company A charges 29 per week plus 13 per kilometer, so cost is $C_A = 29 + 13x$. - Company B charges 85 per week plus 6 per kilometer, so cost is $C_B = 85 + 6x$. 3. **Set up the equation for equal costs:** $$29 + 13x = 85 + 6x$$ 4. **Solve for $x$:** Subtract 6x from both sides: $$29 + \cancel{13x} - \cancel{6x} = 85 + \cancel{6x} - \cancel{6x} \implies 29 + 7x = 85$$ Subtract 29 from both sides: $$29 - 29 + 7x = 85 - 29 \implies 7x = 56$$ Divide both sides by 7: $$\frac{\cancel{7}x}{\cancel{7}} = \frac{56}{7} \implies x = 8$$ 5. **Interpretation:** You must drive 8 kilometers for the rental costs of both companies to be the same. **Final answer:** $x = 8$ kilometers.