Question

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ Simplify the left side of the inequality.

Short answer

The simplified form of the inequality equation would be \(1.06x + 21.2 \leq 58\).

Step-by-step solution

- Distribute the Sales Tax Across the Items

First, apply the sales tax to the items. To do this, multiply 0.06 by \(x\) (the price of jeans) and 20 (the price of the T-shirt). This gives \(0.06x + 1.2\).

- Simplify the Inequality

Next, add the results from the distribution to the original costs of the items. The equation becomes \(x + 20 + 0.06x + 1.2\). Combine like terms and you'll get \(1.06x + 21.2 \leq 58\).