Question

which shows the correct solution to the inequality \\(\frac{7}{10} \geq 1\frac{5}{8} + p\\)?

Explanation:

Step1: Rewrite mixed number

First, rewrite the mixed number \(1\frac{5}{8}\) as an improper fraction. \(1\frac{5}{8}=\frac{1\times8 + 5}{8}=\frac{13}{8}\). The inequality becomes \(\frac{7}{10}\geq\frac{13}{8}+p\).

Step2: Isolate the variable \(p\)

Subtract \(\frac{13}{8}\) from both sides of the inequality. So, \(p\leq\frac{7}{10}-\frac{13}{8}\).

Step3: Find a common denominator

The common denominator of 10 and 8 is 40. Convert the fractions: \(\frac{7}{10}=\frac{7\times4}{10\times4}=\frac{28}{40}\) and \(\frac{13}{8}=\frac{13\times5}{8\times5}=\frac{65}{40}\).

Step4: Subtract the fractions

Now, \(\frac{28}{40}-\frac{65}{40}=\frac{28 - 65}{40}=\frac{- 37}{40}\). So, \(p\leq-\frac{37}{40}\) or \(p\leq - 0.925\).

Answer:

\(p\leq-\frac{37}{40}\) (or \(p\leq - 0.925\))