Rita bakes pies at a bakery. The number of pies she can bake, $x$, is limited by the ingredients they have in stock. This situation is represented by $2 x-3<7$ and $5-x<8$. Solve the compound inequality and write the viable solutions.
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Solution
Step 1 ：The problem is asking for the range of values that \(x\) can take, given the two inequalities \(2x - 3 < 7\) and \(5 - x < 8\). To find this range, we need to solve each inequality separately and then find the intersection of the two solution sets.
Step 2 ：Solving the first inequality, \(2x - 3 < 7\), we get \(x < 5\).
Step 3 ：Solving the second inequality, \(5 - x < 8\), we get \(x > -3\).
Step 4 ：The solution to the compound inequality is the range of values between -3 and 5. However, since the number of pies that Rita can bake cannot be negative, we need to adjust the lower limit to 0.
Step 5 ：So, the solution to the compound inequality is \(0 \leq x \leq 5\).
Step 6 ：Final Answer: Rita can bake between 0 and 5 pies, inclusive. So, the solution to the compound inequality is \(0 \leq x \leq 5\). In Latex format, the final answer is \(\boxed{0 \leq x \leq 5}\).
From Solvely APP
Solution
Step 1 ：The problem is asking for the range of values that \(x\) can take, given the two inequalities \(2x - 3 < 7\) and \(5 - x < 8\). To find this range, we need to solve each inequality separately and then find the intersection of the two solution sets.
Step 2 ：Solving the first inequality, \(2x - 3 < 7\), we get \(x < 5\).
Step 3 ：Solving the second inequality, \(5 - x < 8\), we get \(x > -3\).
Step 4 ：The solution to the compound inequality is the range of values between -3 and 5. However, since the number of pies that Rita can bake cannot be negative, we need to adjust the lower limit to 0.
Step 5 ：So, the solution to the compound inequality is \(0 \leq x \leq 5\).
Step 6 ：Final Answer: Rita can bake between 0 and 5 pies, inclusive. So, the solution to the compound inequality is \(0 \leq x \leq 5\). In Latex format, the final answer is \(\boxed{0 \leq x \leq 5}\).
